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Question: Two identical glass (m<sub>g</sub> = 3/2) equiconvex lenses of focal length 'f' are kept in contact....

Two identical glass (mg = 3/2) equiconvex lenses of focal length 'f' are kept in contact. The space between the two lenses is filled with water . The focal length of the combination is

A

f

B

f/2

C

4f/3

D

3f/4

Answer

3f/4

Explanation

Solution

For water lens

1 F′=(43−1)(1R1−1R2)\frac { 1 } { \mathrm {~F} ^ { \prime } } = \left( \frac { 4 } { 3 } - 1 \right) \left( \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right)

\ 1 F′=13(1−R1−1R)\frac { 1 } { \mathrm {~F} ^ { \prime } } = \frac { 1 } { 3 } \left( \frac { 1 } { - \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } } \right) …(i)

For glass lens

…(ii

(i)/(ii)

̃ F' = – 3f2\frac { 3 \mathrm { f } } { 2 }

\ for 3 lens combination;

̃ F =

w