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 :

Question

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Answer 1

Applying the lens equation, we get

$\frac{1}{v} + \frac{1}{1 0} = \frac{1}{f _{1}}$ ... (1)

For mirror,

$\frac{1}{2 5 . 4} - \frac{1}{4 5 . 8 - 3 2 . 2 - v} = \frac{1}{f _{2}}$

$\frac{1}{2 5 . 4} - \frac{1}{1 3 . 6 - v} = \frac{1}{f _{2}}$ .... (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.

Answer 2

Applying the lens equation, we get

\frac{1}{v} + \frac{1}{1 0} = \frac{1}{f _{1}}

... (1)

For mirror,

\frac{1}{2 5 . 4} - \frac{1}{4 5 . 8 - 3 2 . 2 - v} = \frac{1}{f _{2}}

\frac{1}{2 5 . 4} - \frac{1}{1 3 . 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.

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