question_answer

To find the focal length of a convex mirror, a student records the following data :

Object pin	Convex Lens	Convex Mirror	Image Pin
22.2 cm	32.2 cm	45.8 cm	71.2 cm

The focal length of the convex lens is\[{{f}_{1}}\] and that of mirror is \[{{f}_{2}}.\]Then taking index correction to be negligibly small, \[{{f}_{1}}\]and \[{{f}_{2}}.\] are close to :   JEE Main Online Paper (Held On 09 April 2016)

A) \[{{f}_{1}}=15.6cm\]                       \[{{f}_{2}}=25.4cm\]                

B) \[{{f}_{1}}=7.8cm\]                         \[{{f}_{2}}=12.7cm\]                

C) \[{{f}_{1}}=7.8cm\]                         \[{{f}_{2}}=25.4cm\]                

D) \[{{f}_{1}}=12.7cm\]                       \[{{f}_{2}}=7.8cm\]                

Correct Answer: D

Solution :

                For convex lens i. I u =.10 cm v = 39 cm \[{{f}_{1}}=\frac{uv}{u-v}\] \[=\frac{390}{49}=7.8cm\]For convex mirror \[R=25.4cm\] \[{{f}_{2}}=12.7cm\]