JPH09251132A - Eyepiece zoom lens system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain an eyepiece zoom lens system in which various aberations are satisfactorily corrected with simple and compact constitution while a large zoom ratio and sufficiently long eye relief are secured by providing the system with a first negative lens group, a second positive lens group and a third positive lens group and satisfying a specified condition. SOLUTION: A variable power action is executed by moving the first lens group G1 having negative refractive power and the second lens group G2 having positive refractive power in mutually reverse directions by interposing an object image I formed by an objective lens system and the first lens group G1. Then, the variable power action is provided with a larger variable power ratio then 2. The second lens group G2 is provided with a positive lens component L2 whose surface on an eye point side is provided with stronger curvature than the surface thereof on an object side. Then, when the radius of the curvature of the component L2 on the object side is defined as (ra) and the radius of the curvature thereof on the eye point side is defined as (rb), the condition of -1.0<=(rb+ra)/(rb-ra)<=0.7 is satisfied. Thus, the simple, compact and high- performance lens system constituted of three groups being five lenses is obtained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an eyepiece zoom lens system, and more particularly to a zoom lens system used for eyepiece lenses such as telescopes and binoculars.

[0002]

2. Description of the Related Art Generally, a movable space for a lens group is required to construct a zoom lens system. Therefore, in the zoom lens system, the total length of the lens system tends to be large, and it is difficult to make a compact structure. Further, if the refracting power of each lens group is increased in order to make the zoom lens system compact, the amount of aberration will increase. This tendency becomes more remarkable as the zoom ratio (zoom ratio) of the zoom lens system increases. As a conventional eyepiece zoom lens system, for example, JP-A-53-51757 and JP-A-Sho-6.
A zoom lens system disclosed in JP-A-2-134617 is known.

[0003]

[Problems to be Solved by the Invention] Japanese Patent Application Laid-Open No. 53-5175
The eyepiece zoom lens system disclosed in Japanese Patent Publication No. 7 certainly secures some good performance. However, this zoom lens system has a lens configuration of 6 elements in 4 groups, and the number of lenses is too large. In addition, although the zoom ratio is 2, the total length of the lens system is relatively long. On the other hand, JP
The eyepiece zoom lens system disclosed in Japanese Patent No. 134617 has three components.
It has a simple lens configuration of five elements. However, like the eyepiece zoom lens system disclosed in JP-A-53-51757, the total length of the lens system is relatively large.

In any of the eyepiece zoom lens systems described in any of the publications, distortion is still 6% in each focal length region other than the longest focal length state of the eyepiece zoom lens system.
About 9% remains. Further, in the eyepiece zoom lens system having a zoom ratio larger than 2, distortion aberration larger than 10% remains. As described above, in the conventional eyepiece zoom lens system, it is difficult to correct the distortion when the zoom ratio exceeds 2. Further, in the conventional technology, a wider movable space is required as the zoom ratio becomes larger, and it is difficult to make the zoom lens system compact.

The present invention has been made in view of the above-mentioned problems, and has an eyepiece zoom that has a simple and compact lens structure while ensuring a zoom ratio larger than 2, and that various aberrations are favorably corrected. It is intended to provide a lens system.

[0006]

In order to solve the above problems, in the present invention, a first lens group G1 having a negative refracting power and a second lens group G2 having a positive refracting power in order from the object side. And a third lens group G3 having a positive refractive power, the first lens group G1 and the second lens group G2 move in opposite directions along the optical axis during zooming,
In the eyepiece zoom lens system having a zoom ratio greater than 2, the second lens group G2 has a positive lens component L in which the eyepoint side surface has a stronger curvature than the object side surface.
2 and the radius of curvature of the object side surface of the positive lens component L2 is ra and the radius of curvature of the eye point side surface of the positive lens component L2 is rb, then −1.0 ≦ (rb + ra) There is provided an eyepiece zoom lens system characterized by satisfying a condition of /(rb-ra)≦−0.7.

According to a preferred embodiment of the present invention, the shortest focal length of the eyepiece zoom lens system is fM,
The focal length of the lens group G1 is f1, the focal length of the second lens group G2 is f2, the focal length of the third lens group G3 is f3, and the first lens group G1 and the second lens group G2 are Is S1 and the principal point interval between the second lens group G2 and the third lens group G3 is S2, 2.3 <| f1 / fM | <5.7 2.2 <f2 / FM <4.6 2.6 <f3 / fM <5.4 3.4 <S1 / fM <6.4 0.05 <S2 / fM <0.7.

[0008]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a diagram showing the refractive power arrangement of an eyepiece zoom lens system of the present invention in a thin-walled system, in which (A) is the longest focal length state as an eyepiece zoom lens system (as a telescope). (Low magnification state), (B) shows an intermediate focal length state, and (C) shows a shortest focal length state as an eyepiece zoom lens system (high magnification state as a telescope). In FIG. 1, EP represents an eye point, and I represents an object image formed through the objective lens system and the first lens group G1.

As shown in FIG. 1, a first lens group G1 having a negative refractive power and a second lens group having a positive refractive power are sandwiched by an object image I formed by an objective lens system (not shown) and a first lens group G1. By moving the lens group G2 and the lens group G2 in opposite directions,
Magnification is changed. Then, as shown in the figure, as the focal length of the eyepiece zoom lens system becomes shorter, that is, (A)
The first lens group G1 and the second lens group G2 move so that the distance between the first lens group G1 and the second lens group G2 increases as the state changes from (1) to (C).

According to the present invention, in the above configuration,
The second lens group G2 has a positive lens component L2, and the positive lens component L2 satisfies the following conditional expression (1). −1.0 ≦ (rb + ra) / (rb−ra) ≦ −0.7 (1) where ra: radius of curvature of object-side surface of positive lens component L2 rb: eyepoint side of positive lens component L2 Radius of curvature of face

As described above, with the configuration in which the lens surface on the eyepoint side has a stronger curvature than the lens surface on the object side, one positive lens component L2 constitutes the second lens group G2 and a strong power ( It is possible to satisfactorily correct aberration fluctuations due to zooming, such as distortion and astigmatism, while ensuring the (refractive power). If the upper limit of conditional expression (1) is exceeded, astigmatism and distortion will increase, and coma will also increase. On the other hand, when the value goes below the lower limit of conditional expression (1), astigmatism and distortion increase.

In order to further correct chromatic aberration, it is preferable that one positive lens component L2 constituting the second lens group G2 is composed of a cemented lens. In this case, it goes without saying that the object-side lens surface and the eyepoint-side lens surface of the positive lens component L2 formed of the cemented lens need to satisfy the conditional expression (1) according to the present invention. However, in normal use, the single positive lens component L2 forming the second lens group G2 is not provided with a cemented surface, and a single biconvex lens satisfying conditional expression (1) is used as the second lens group G2. Can also be configured.

Further, in the present invention, it is desirable that the following conditional expressions (2) to (6) are satisfied. 2.3 <| f1 / fM | <5.7 (2) 2.2 <f2 / fM <4.6 (3) 2.6 <f3 / fM <5.4 (4) 3.4 <S1 / fM <6.4 (5) 0.05 <S2 / fM <0.7 (6)

Here, fM: shortest focal length as an eyepiece zoom lens system f1: focal length of the first lens group G1 f2: focal length of the second lens group G2 f3: focal length of the third lens group G3 S1: first Principal point spacing between the first lens group G1 and the second lens group G2 S2: Principal point spacing between the second lens group G2 and the third lens group G3

In the conditional expressions (2) to (4), the focal lengths f1 to f3 of each lens group are standardized by the shortest focal length fM as the eyepiece zoom lens system, so that an appropriate power distribution to each lens group is achieved. Stipulates. Conditional expression (2)
When the value exceeds the upper limit of, the negative refractive power of the first lens group G1 becomes weak, and it is necessary to make the refractive power of the second lens group G2 relatively strong in order to make the focal length of the eyepiece zoom lens system a predetermined value. There is. As a result, the refracting power of the second lens group G2 becomes too strong, causing an increase in distortion and astigmatism. On the other hand, when the value goes below the lower limit of the conditional expression (2), coma aberration, particularly coma aberration in a state where the focal length of the eyepiece zoom lens system is long, increases, which makes it difficult to correct aberrations satisfactorily.

If the upper limit of conditional expression (3) is exceeded, the refracting power of the second lens group G2 will weaken and the amount of movement of the second lens group G2 for zooming will increase. Therefore, when the second lens group G2 moves for zooming, the first lens group G1
And the object image I formed between the second lens group G2 and the second lens group G2. As a result, scratches and dust on the lens surface of the second lens group G2 become noticeable in the observation visual field, which is not preferable. On the other hand, when the value goes below the lower limit of the conditional expression (3), the refracting power of the second lens group G2 becomes too strong, which causes an increase in various aberrations such as distortion and astigmatism, thereby simplifying the lens configuration. Becomes difficult.

When the value exceeds the upper limit of the conditional expression (4), the refracting power of the third lens group G3 becomes too weak, which makes it difficult to correct coma and chromatic aberration in aberration correction.
It becomes impossible to have a simple lens configuration.
On the other hand, when the value goes below the lower limit of conditional expression (4), the refracting power of the third lens group G3 becomes strong, and the zooming effect of the second lens group G2 becomes small. As a result, the first lens group G for zooming
The load of 1 becomes excessively large, and the first lens group G1 crosses the object image I during zooming, so that scratches and dust on the lens surface easily appear in the visual field. Further, the burden of the first lens group G1 on the aberration correction becomes too large, which makes it difficult to balance the aberration correction.

Conditional expression (5) is defined by the first lens group G1 and the second lens group G1.
An appropriate range is defined for the principal point spacing S1 with the lens group G2. If the upper limit of conditional expression (5) is exceeded, the overall length of the eyepiece zoom lens system becomes long, and it becomes impossible to realize a compact structure. Further, in order to secure a predetermined focal length as the eyepiece zoom lens system, the negative refracting power of the first lens group G1 is weakened. As a result, the amount of zoom movement of the first lens group G1 increases, and the first lens group G1 easily crosses the object image I, which is not preferable. On the other hand, when the value goes below the lower limit of conditional expression (5), the moving space of each lens unit for zooming becomes small, and it becomes difficult to secure a sufficient zooming region.

Conditional expression (6) is defined by the second lens group G2 and the third lens group G2.
An appropriate range is defined for the principal point spacing S2 with the lens group G3. When the upper limit of conditional expression (6) is exceeded, the principal point spacing S2 between the second lens group G2 and the third lens group G3 becomes large. As a result, the aperture of the second lens group G2 becomes too large, which makes it difficult to correct aberrations. On the other hand, when the value goes below the lower limit of the conditional expression (6), the second lens group G2 and the third lens group G2
The distance between the lens group G3 and the lens group G3 becomes smaller, and it is the second for power distribution.
It becomes necessary to weaken the refractive power of the lens group G2.
As a result, the conditional expression (3) cannot be satisfied, which is not preferable.

Further, in the present invention, the first lens group G
Reference numeral 1 denotes, in order from the object side, a cemented negative lens of a positive meniscus lens L1p and a biconcave lens L1n, or a biconcave lens L1n.
And a positive meniscus lens L1p are cemented negative lenses, and the third lens group G3 has, in order from the object side, a cemented positive lens cemented with a biconvex lens L3p and a negative meniscus lens L3n, and the following conditional expression (7) is satisfied. It is desirable to satisfy (8) and (8). 40 <ν1 (7) ν3 <40 (8)

Where ν1: Abbe number of the biconcave lens L1n in the first lens group G1 ν3: Abbe number of the negative meniscus lens L3n in the third lens group G3 Thus, the first lens group G1 has a positive meniscus It is desirable that the cemented biconcave lens is formed by bonding the lens L1p and the biconcave lens L1n together. Even if either the positive meniscus lens L1p or the biconcave lens L1n is arranged on the eyepoint side, the same performance can be maintained. it can. The third lens group G3 is fixed along the optical axis during zooming and has a biconvex lens L3p, as will be described later in Examples.
And negative meniscus lens L with convex surface facing the eyepoint side
It is preferably composed of a biconvex lens cemented with 3n.

Conditional expression (7) defines a condition for reducing the variation of chromatic aberration due to zooming. Conditional expression (7)
Below the lower limit of, the burden of chromatic aberration correction on the second lens group G2 and the third lens group G3 increases,
The lens configuration becomes complicated. In this case, the chromatic aberration can be corrected by weakening the negative refractive power of the first lens group G1, but this is not preferable because it deviates from the range of the conditional expression (4).

Conditional expression (8) defines a condition for favorably correcting chromatic aberration without reducing the radius of curvature of the cemented surface of the cemented positive lens constituting the third lens group G3. By satisfying the conditional expression (8), it becomes possible to make the configurations of the first lens group G1 and the second lens group G2 compact.

[0024]

Embodiments of the present invention will be described below with reference to the accompanying drawings. In each embodiment, the eyepiece zoom lens system of the present invention includes, from the object side, in order from the object side, a first lens group G1 having a negative refractive power, a second lens group G2 having a positive refractive power, and Third lens group G having positive refractive power
3 is provided. Then, upon zooming, the first lens group G1 and the second lens group G2 move in opposite directions along the optical axis.

[First Embodiment] FIG. 2 is a view showing the lens arrangement of an eyepiece zoom lens system according to the first embodiment of the present invention. The eyepiece zoom lens system of FIG.
A first lens group G1 made up of a cemented biconcave lens composed of a positive meniscus lens L1p having a concave surface facing the object side and a biconcave lens L1n.
And a second lens group G2 composed of a biconvex lens L2, and a third lens group G3 composed of a biconvex lens cemented with a biconvex lens L3p and a negative meniscus lens L3n having a concave surface facing the object side. In FIG. 2, EP is an eye point, I is an object image formed through the objective lens system and the first lens group G1, and I ′ is a virtual image by the eyepiece zoom lens system (object by the objective lens system alone). Image). 2 shows the position of each lens group in the shortest focal length state as the eyepiece zoom lens system (high magnification state as the telescope). That is, the lens arrangement of FIG. 2 corresponds to the state of FIG. Therefore, upon zooming to the longest focal length state, as shown in FIG. 1, the first lens group G1 and the second lens group G2 are
Moves along the optical axis, and the third lens group G3 is fixed along the optical axis.

The following table (1) lists the values of specifications of the first embodiment of the present invention. In Table (1), f is the focal length of the eyepiece zoom lens system, 2ω is the angle of view (apparent field of view) of the eyepiece zoom lens system, Z is the zoom ratio, and back focus Bf is ray tracing from the eyepoint side. In this case, the distances along the optical axis between the final surface of the eyepiece zoom lens system (the surface on the object side of the first lens group G1 in this embodiment) and the virtual image I ′ are shown. In Table (1), the leftmost number indicates the order of the lens surfaces from the object side, r
Is the radius of curvature of each lens surface, d is the distance between each lens surface, n
And ν respectively indicate the refractive index and the Abbe number for the d line (λ = 587.6 nm).

[0027]

[Table 1] f = 5.2 to 12.9 2ω = 52.0 to 34.0 ° Z = 2.48 (Values corresponding to conditions) f1 = -17 f2 = 18.8 f3 = 23 fM = 5.2 (1) (rb + ra) / (rb-ra) =-0.713 (2) | f1 / fM | = 3. 269 (3) f2 / fM = 3.615 (4) f3 / fM = 4.423 (5) S1 / fM = 4.927 (6) S2 / fM = 0.108 (7) v1 = 61.1 ( 8) ν3 = 27.6

3 to 5 are aberration diagrams of the first embodiment. FIG. 3 shows various aberrations in the longest focal length state (low magnification state as a telescope) of the eyepiece zoom lens system,
FIG. 4 shows various aberrations in the intermediate focal length state as the eyepiece zoom lens system, and FIG. 5 shows various aberrations in the shortest focal length state as the eyepiece zoom lens system (high magnification state as the telescope). Each aberration is an aberration when ray tracing is performed from the eye point side.

In each aberration diagram, FNO is the F number,
ω is the half angle of view (half the apparent field of view: the unit is degrees), and d
Is the d-line (λ = 587.6 nm) and C is the C-line (λ = 65 nm).
6.3 nm) and F indicates the F line (λ = 486.1 nm). Thus, in order to show the correction state of chromatic aberration with respect to spherical aberration, astigmatism and coma,
In addition to the aberration amount for the d-line which is the reference ray, the aberration amounts for the C-line and F-line are also shown. In the aberration diagram showing astigmatism, the solid line S indicates the sagittal image plane, and the broken line M indicates the meridional image plane. As is clear from each aberration diagram, in this example, it is found that various aberrations are satisfactorily corrected over the entire zooming region from the shortest focal length state to the longest focal length state.

[Second Embodiment] FIG. 6 is a view showing the lens arrangement of an eyepiece zoom lens system according to the second embodiment of the present invention. The eyepiece zoom lens system of FIG.
First lens group G1 including a cemented biconcave lens L1n and a positive meniscus lens L1p having a concave surface facing the object side
And a second lens group G2 composed of a biconvex lens L2, and a third lens group G3 composed of a biconvex lens cemented with a biconvex lens L3p and a negative meniscus lens L3n having a concave surface facing the object side. In FIG. 2, EP is an eye point, I is an object image formed through the objective lens system and the first lens group G1, and I ′ is a virtual image by the eyepiece zoom lens system (object by the objective lens system alone). Image). Note that FIG. 6 shows the position of each lens group in the shortest focal length state as the eyepiece zoom lens system (high magnification state as the telescope). That is, the lens arrangement of FIG. 6 corresponds to the state of FIG. Therefore, upon zooming to the longest focal length state, as shown in FIG. 1, the first lens group G1 and the second lens group G2 are
Moves along the optical axis, and the third lens group G3 is fixed along the optical axis.

Table 2 below summarizes data values of the second embodiment of the present invention. In Table (2), f is the focal length of the eyepiece zoom lens system, 2ω is the angle of view (apparent field of view) of the eyepiece zoom lens system, Z is the zoom ratio, and back focus Bf is ray tracing from the eyepoint side. In this case, the distances along the optical axis between the final surface of the eyepiece zoom lens system (the surface on the object side of the first lens group G1 in this embodiment) and the virtual image I ′ are shown. In Table (2), the leftmost number indicates the order of the lens surfaces from the object side, r
Is the radius of curvature of each lens surface, d is the distance between each lens surface, n
And ν respectively indicate the refractive index and the Abbe number for the d line (λ = 587.6 nm).

[0032]

[Table 2] f = 6.4 to 15.4 2ω = 52.0 to 34.0 ° Z = 2.41 (Values corresponding to conditions) f1 = -30 f2 = 20.5 f3 = 23 fM = 6.4 (1) (rb + ra) / (rb-ra) =-0.719 (2) | f1 / fM | = 4. 688 (3) f2 / fM = 3.203 (4) f3 / fM = 3.594 (5) S1 / fM = 4.897 (6) S2 / fM = 0.188 (7) ν1 = 64.1 ( 8) ν3 = 27.6

7 to 9 are various aberration diagrams of the second embodiment. FIG. 7 shows various aberrations in the longest focal length state as an eyepiece zoom lens system (low magnification state as a telescope),
FIG. 8 shows various aberrations in the intermediate focal length state as the eyepiece zoom lens system, and FIG. 9 shows various aberrations in the shortest focal length state as the eyepiece zoom lens system (high magnification state as the telescope). Each aberration is an aberration when ray tracing is performed from the eye point side.

In each aberration diagram, FNO is the F number,
ω is the half angle of view (half the apparent field of view: the unit is degrees), and d
Is the d-line (λ = 587.6 nm) and C is the C-line (λ = 65 nm).
6.3 nm) and F indicates the F line (λ = 486.1 nm). Thus, in order to show the correction state of chromatic aberration with respect to spherical aberration, astigmatism and coma,
In addition to the aberration amount for the d-line which is the reference ray, the aberration amounts for the C-line and F-line are also shown. In the aberration diagram showing astigmatism, the solid line S indicates the sagittal image plane, and the broken line M indicates the meridional image plane. As is clear from each aberration diagram, in this example, it is found that various aberrations are satisfactorily corrected over the entire zooming region from the shortest focal length state to the longest focal length state.

As described above, in the eyepiece zoom lens system of each of the embodiments described above, the zoom ratio is about 2.5, the angle of view (apparent field of view) is 52 ° to 34 °, and it is simple and compact with 5 elements in 3 groups Achieves a unique lens configuration. Then, although the zoom ratio exceeds 2, various aberrations, particularly distortion aberration, are well corrected. In each of the above-mentioned embodiments,
Although the angle of view (apparent field of view) is set to 52 ° to 34 °, the angle of view (apparent field of view) can be expanded to about 60 ° unless the effective diameter of the eyepiece zoom lens system is limited. . Further, although the above-mentioned embodiments relate to the eyepiece zoom lens system, it is obvious that the present invention can be applied to a monofocal eyepiece lens system.

[0036]

As described above, according to the present invention, while maintaining a zoom ratio larger than 2, a simple and compact lens configuration of 5 elements in 3 groups is provided, and various aberrations are favorably corrected. A high-performance eyepiece zoom lens system can be realized.

[Brief description of drawings]

FIG. 1 is a diagram showing a refractive power arrangement of an eyepiece zoom lens system of the present invention in a thin system, in which (A) is a longest focal length state as an eyepiece zoom lens system (a low magnification state as a telescope).
(B) shows an intermediate focal length state, and (C) shows a shortest focal length state as an eyepiece zoom lens system (high magnification state as a telescope).

FIG. 2 is a diagram showing a lens configuration of an eyepiece zoom lens system according to Example 1 of the present invention.

FIG. 3 is a diagram of various types of aberration in the longest focal length state (low magnification state as a telescope) of the eyepiece zoom lens system of Example 1.

FIG. 4 is a diagram of various types of aberration in the intermediate focal length state as the eyepiece zoom lens system of Example 1.

FIG. 5 is a diagram of various types of aberration in the shortest focal length state (high magnification state as a telescope) of the eyepiece zoom lens system of Example 1.

FIG. 6 is a diagram showing a lens configuration of an eyepiece zoom lens system according to Example 2 of the present invention.

FIG. 7 is a diagram of various types of aberration in the longest focal length state (low magnification state as a telescope) of the eyepiece zoom lens system of Example 2.

FIG. 8 is a diagram of various types of aberration in the intermediate focal length state as the eyepiece zoom lens system of Example 2.

FIG. 9 is a diagram of various types of aberration in the shortest focal length state (high magnification state as a telescope) of the eyepiece zoom lens system of Example 2.

[Explanation of symbols]

 G1 1st lens group G2 2nd lens group G3 3rd lens group Li Each lens component EP Eye point I Object image I'Virtual image

Claims (3)

[Claims] 1. A first lens group G1 having a negative refractive power and a second lens group G having a positive refractive power in order from the object side.
2 and a third lens group G3 having a positive refractive power,
In the eyepiece zoom lens system having a zoom ratio greater than 2, the first lens group G1 and the second lens group G2 move in opposite directions along the optical axis upon zooming, and the second lens The group G2 has a positive lens component L2 in which the surface on the eyepoint side has a stronger curvature than the surface on the object side, and the radius of curvature of the object side surface of the positive lens component L2 is ra, and the positive lens An eyepiece zoom lens system characterized by satisfying the condition of −1.0 ≦ (rb + ra) / (rb−ra) ≦ −0.7, where rb is the radius of curvature of the surface of the component L2 on the eyepoint side. . 2. The minimum focal length of the eyepiece zoom lens system is fM, and the focal length of the first lens group G1 is f1.
The focal length of the second lens group G2 is f2, the focal length of the third lens group G3 is f3, and the principal point distance between the first lens group G1 and the second lens group G2 is S1.
And S2 is the principal point distance between the second lens group G2 and the third lens group G3, 2.3 <| f1 / fM | <5.7 2.2 <f2 / fM <4.6 The eyepiece according to claim 1, wherein the condition of 2.6 <f3 / fM <5.4 3.4 <S1 / fM <6.4 0.05 <S2 / fM <0.7 is satisfied. Zoom lens system. 3. The first lens group G1 includes, in order from the object side, a negative lens cemented with a positive meniscus lens L1p and a biconcave lens L1n or a biconcave lens L1n and a positive meniscus lens L.
The third lens group G3 has a cemented positive lens cemented with a biconvex lens L3p and a negative meniscus lens L3n in order from the object side, and the third lens group G3 has a cemented positive lens cemented with it. The condition of 40 <ν1 ν3 <40 is satisfied when the Abbe number of the concave lens L1n is ν1 and the Abbe number of the negative meniscus lens L3n in the third lens group G3 is ν3. Alternatively, the eyepiece zoom lens system according to the item 2.