Question 55: Ray Optics

Question

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L
1
, L
2
by AB plane and L
3
, L
4
by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L
1
and L
3
is
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m6qjfvok/2d924479-0574-436a-ad8a-ac199cba2c7f/1bd24e40-e2ff-11ef-9d65-2b094293796d/file-jaoe38c1m6qjfvol.png?format=png)

Accepted Answer

Here,
we will use lens maker formula,
${1 \over f} = \left( {\mu  - 1} ight)\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} ight)$
So, the focal length of L$_1$ remains the same as the original lens because the curvature of the surfaces does not change
So, ${\left( f ight)_{{L_1}}} = f$ .... (1)
Now, for L$_3$, L$_3$ is plano-convex lens
${R_1} = R,\,{R_2} = \infty $
So, ${1 \over {{{\left( f ight)}_{{L_3}}}}} = \left( {\mu  - 1} ight)\left( {{1 \over R} - {1 \over \infty }} ight)$
$ \Rightarrow {1 \over {{{\left( f ight)}_{{L_3}}}}} = \left( {\mu  - 1} ight){1 \over R}$ ..... (2)
For whole double convex lens,
${1 \over f} = \left( {\mu  - 1} ight)\left( {{1 \over R} - {1 \over { - R}}} ight)$ (As ${R_1} = R$, ${R_2} =  - R$)
$ \Rightarrow {1 \over f} = \left( {\mu  - 1} ight)\left( {{1 \over R} + {1 \over R}} ight)$
$ \Rightarrow {1 \over f} = \left( {\mu  - 1} ight)\left( {{2 \over R}} ight)$ .... (3)
From (2) and (3),
${1 \over {{{\left( f ight)}_{{L_3}}}}} = {1 \over {2f}} \Rightarrow {\left( f ight)_{{L_3}}} = 2f$
Hence, ${{{{\left( f ight)}_{{L_1}}}} \over {{{\left( f ight)}_{{L_3}}}}} = {f \over {2f}} \quad	ext{....(from (1)})\quad= 1:2$
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m6xrhv3r/b4e2fba8-c1c3-416a-932c-22a04dba18c6/18928c70-e6f8-11ef-b104-c92cb842bf9b/file-jaoe38c1m6xrhv3s.png?format=png)

Answer

1 : 2

Answer

1 : 1

Answer

2 : 1

Answer

1 : 4

Ray Optics

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L 1 , L 2 by AB plane and L 3 , L 4 by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L 1 and L 3 is

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