Question

In a medium of refractive index 1.6 and having a convex surface has a point object in it at a distance of 12cm from the pole.the radius of curvature is 6cm.locate the image as seen from air?

Answer 1

Answer on Question#39363, Physics, Optics

In a medium of refractive index 1.6 and having a convex surface has a point object in it at a distance of $12\mathrm{cm}$ from the pole. The radius of curvature is $6\mathrm{cm}$ . Locate the image as seen from air?

Solution:

In this figure:

C is the center of curvature of the spherical surface

R is the radius of curvature

is the position of the Object

I is the position of the Image

- $S_{o}$ is the distance of the object from the surface along the optical axis

- $S_{i}$ is the distance from the surface to the Image

For light rays going from medium 1 $(\mathsf{n}_1)$ to medium 2 $(\mathsf{n}_2)$ :

$$\frac {n _ {1}}{s _ {o}} + \frac {n _ {2}}{s _ {i}} = \frac {n _ {2} - n _ {1}}{R}$$

Given: $n_1 = 1$ , $n_2 = 1.6$ , $R = 6 \, \text{cm}$ , $s_i = 12 \, \text{cm}$ .

$$\begin{array}{l} \frac{n_{2}}{s_{i}} + \frac{n_{1}}{s_{i}^{\prime}} = \frac{n_{2} - n_{1}}{R} \\ \frac{1.6}{12} + \frac{1}{s_{i}^{\prime}} = \frac{0.6}{6} \\ \frac{1}{s_{o}} = \frac{0.6}{6} - \frac{1.6}{12} = -\frac{0.4}{12} \\ s_{o} = -30 \text{ cm} \end{array}$$

Hence the object appears 30 cm deep from the curved side.

Answer. 30 cm