Question

An object starts moving at an angle of ${45}^{\circ }$ with the principal axis as shown in Figure in front of a biconvex lens of focal length $+10\text{cm}$. If $\theta$ denotes the angle at which image starts to move with principal axis. then

• A. $\theta =\frac{3\pi }{4}$
• B. $\theta =\frac{\pi }{2}$
• C. $\theta =\frac{\pi }{3}$
• D. $\theta =\frac{\pi }{4}$

Answer 1

The correct option is D $\theta =\frac{\pi }{4}$

When Object is at $2f$ distance from pole of lens , image is also formed at $2f$ distance from pole on the opposite side of lens.


In the given situation, lens is stationary.

So, we can say that,

${\overrightarrow{v}}_I=m^2\times {\overrightarrow{v}}_O$

For the given situation, Lateral magnification , $m=1$

$\therefore {\overrightarrow{v}}_I={\overrightarrow{v}}_O$

Thus, $|v_{Iy}|=|v_{Oy}|$ and $|v_{Ix}|=|v_{ox}|$

Hence, option (d) is the correct answer.