Question

Comprehension
Two thin similar spherical glass pieces of radius $40\text{cm}$ are joined together front to front with rear portion of one piece silvered and the combination of glass pieces is placed at a distance $60\text{cm}$ from a screen. A point object is placed on the optical axis of the combination at the mid point of the line joining this combination and screen. Initially there is air between glass pieces as well as between combination and screen.


The distance through which the object must be displaced so that the sharp image is again formed on screen is:

• A. $20\text{cm}$ towards the combination
• B. $20\text{cm}$ away from the combination
• C. $15\text{cm}$ towards the combination
• D. $15\text{cm}$ away from the combination

Answer 1

The correct option is C $15\text{cm}$ towards the combination

Given :- $f=-12\text{cm}$
Let the distance of the object from the combination is $u$.

$\Rightarrow v=-60\text{cm}$
Applying mirrors formula :-
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\frac{1}{-12}=\frac{1}{-60}+\frac{1}{u}$
$\frac{1}{u}=\frac{1}{60}-\frac{1}{12}=\frac{-4}{60}$
$u=-15\text{cm}$
So, object should be shifted by :-
Shift $=$ old distance $-$ new distance
$=30-15=15\text{cm}$ towards the combination.