Question

Two identical glass (m_g = 3/2) equiconvex lenses of focal length f are kept in contact. The space between the two lenses is filled with water (m_w = 4/3). The focal length of the combination is –

• A. f
• B. $\frac { \mathrm { f } } { 2 }$
• C.
• D. $\frac { 3 \mathrm { f } } { 4 }$

Answer 1

Answer: (D)

$\frac { 3 \mathrm { f } } { 4 }$

Answer 2

For water lens

$\frac { 1 } { \mathrm {~F} ^ { \prime } } = \left( \frac { 4 } { 3 } - 1 \right) \left( \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right)$

\ $\frac { 1 } { \mathrm {~F} ^ { \prime } } = \frac { 1 } { 3 } \left( \frac { 1 } { - \mathrm { R } } - \frac { 1 } { \mathrm { R } } \right)$ ……(i)

For glass lens

…….(ii)

(i)/(ii)

$\frac { \frac { 1 } { \mathrm {~F} ^ { \prime } } } { \frac { 1 } { \mathrm { f } } } = - \frac { \frac { 1 } { 3 } } { \frac { 1 } { 2 } } \Rightarrow \frac { \mathrm { f } } { \mathrm { F } ^ { \prime } } = - \frac { 2 } { 3 }$

\ for '3' lens combination.