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  • Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is : <img alt="" src="https://cdn.entrance360.com/media/uploads/2022

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :
 
Option: 1 55.44 cm
Option: 2 9.52 cm
Option: 3 18.23 cm  
Option: 4 37.58 cm

Answers (1)

best_answer

\begin{aligned} &u=-40 \mathrm{~cm} \\ &R=-25 \mathrm{~cm} \end{aligned}

By using the formula for spherical surface

\begin{aligned} &\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R} \\ &\frac{1.4}{v}-\frac{1.25}{(-40)}=\frac{1.4-1.25}{-25} \end{aligned}

         \begin{aligned} & \frac{1.4}{v}=\frac{0.15}{-25}-\frac{1.25}{40} \\ &\frac{1.4}{v}=-\frac{0.03}{5}-\frac{1}{32} \end{aligned}

\begin{aligned} \frac{1.4}{v} &=\frac{-0.96-5}{160}=\frac{-5.96}{160} \\ v &=\frac{-160 \times 1.4}{5.96} \\ v &=-37.58 \mathrm{~cm} \end{aligned}

The correct option is (4)

Image is formed on the left as shown in the figure.

Posted by

vishal kumar

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