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 - I f is the final image formed after all the refractions and reflections-A- If d 1-120 cm- then the - I f - is formed on - O - for any value of d 2-B- If d 1-240 cm- then the - I f - is formed on - O - only if d 2-360 cm-C- If d 1-240 cm- then the - I f - is formed on - O - for all values of d 2-D- If d 1-240 cm- then the - I f- can-t be formed on - O -

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In the figure...

Question

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 60cm. $I_{f}$ is the final image formed after all the refractions and reflections.

If $d_{1} = 120 c m$ , then the ‘ $I_{f}$ ’ is formed on ‘O’ for any value of $d_{2}$ .

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If $d_{1} = 240 c m$ , then the ‘ $I_{f}$ ’ is formed on ‘O’ only if $d_{2} = 360 c m$ .

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If $d_{1} = 240 c m$ , then the ‘ $I_{f}$ ’ is formed on ‘O’ for all values of $d_{2}$ .

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If $d_{1} = 240 c m$ , then the ‘ $I_{f}$ ’ can’t be formed on ‘O’.

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Solution

The correct options are
A
If $d_{1} = 120 c m$ , then the ‘ $I_{f}$ ’ is formed on ‘O’ for any value of $d_{2}$ .

B
If $d_{1} = 240 c m$ , then the ‘ $I_{f}$ ’ is formed on ‘O’ only if $d_{2} = 360 c m$ .

For $d_{1} = 120 c m$

$\frac{μ_{2}}{v} - \frac{μ_{1}}{v} = \frac{μ_{2} - μ_{1}}{R}$

$\Rightarrow \frac{3}{2 v} + \frac{1}{120} = \frac{(\frac{3}{2} - 1)}{60}$

$v = \infty$

$∴$ final image at O, for any value of $d_{2}$

For $d_{1} = 240 c m$

$\Rightarrow \frac{3}{2 v} + \frac{1}{240} = \frac{1}{120}$

$v = 360 c m$

$∴$ final image at O, if $d_{2} = 360 c m$

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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 60cm. If is the final image formed after all the refractions and reflections.

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 60cm. $I_{f}$ is the final image formed after all the refractions and reflections.