In the figure shown,a point object O is place | vedclass

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(A) For the rays to retrace their path,they must strike the plane mirror normally. This means the rays must become parallel to the principal axis afte

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If $d_1 = 120\, cm$,then the $I_f$ is formed on $O$ for any value of $d_2$.

Vedclass · Answer

(A) For the rays to retrace their path,they must strike the plane mirror normally. This means the rays must become parallel to the principal axis after refraction at the spherical surface.Using the refraction formula at a spherical surface: $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,$\mu_1 = 1$ (air),$\mu_2 = 1.5$ (glass),$R = +60\, cm$ (convex surface),and for parallel rays,$v = \infty$.$\frac{1.5}{\infty} - \frac{1}{-d_1} = \frac{1.5 - 1}{60} \implies \frac{1}{d_1} = \frac{0.5}{60} = \frac{1}{120}$.Thus,$d_1 = 120\, cm$. If $d_1 = 120\, cm$,the rays become parallel to the principal axis after refraction,strike the plane mirror normally,and retrace their path to form the image at $O$,regardless of the distance $d_2$.Therefore,statement $(A)$ is correct.

In the figure shown,a point object $O$ is placed in air on the principal axis. The radius of curvature of the spherical surface is $60\, cm$. Let $I_f$ be the final image formed after all the refractions and reflections. Which of the following statements is correct?

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