Question

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

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

• A. $f_1=7.8cm{f}_2=12.7cm$
• B. $f_1=7.8cm{f}_2=25.4cm$
• C. $f_1=15.6cm{f}_2=25.4cm$
• D. $f_1=12.7cm{f}_2=7.8cm$

Answer 1

Answer: (A)

Applying the lens equation, we get

$\frac{1}{v}+\frac{1}{10}=\frac{1}{f_1}$ ... (1)

For mirror,

$\frac{1}{25.4}-\frac{1}{45.8-32.2-v}=\frac{1}{f_2}$

$\frac{1}{25.4}-\frac{1}{13.6-v}=\frac{1}{f_2}$ .... (2)

Since there are 3 variables and only two equations (1) and (2) therefore only by substituting $f_1$ & $f_2$ from options correct values can be verified.

Eliminating $v$ from the equation (1), we get a relation between $f_1$ and $f_2$. This relation is satisfied only by option A.