91Ó°ÊÓ

$\begin{array}{l}{n}_1=10\\ n_2=1.5\\ r=+3\mathrm{cm}\\ i=400\mathrm{cm}\end{array}$

The index of refraction of object and image, the image distance, and the radius of curvature are given in the problem. Using this data and equation, find the object distance and check whether the image is real or virtual and find the position of the image.

Formulae are as follows:

$\frac{{\mathbf{n}}_{\mathbf{1}}}{\mathbf{p}}\mathbf{+}\frac{{\mathbf{n}}_{\mathbf{2}}}{\mathbf{i}}\mathbf{=}\frac{{\mathbf{n}}_{\mathbf{2}}\mathbf{-}{\mathbf{n}}_{\mathbf{1}}}{\mathbf{T}}$

where p is the pole and i is the image distance.

(a)

The index of refractionon the other side of the refracting surfaceis given in the table 34-5. So,$n_2=1.5$

Therefore, the index of refraction on the other side of the refracting surface is 1.5.

b)

From equation 34-8

$\frac{n_1}{p}+\frac{n_2}{i}=\frac{n_2-n_1}{r}$

Rearranging the terms,

role="math" localid="1663048347048" $\begin{array}{l}\frac{n_1}{p}=\frac{n_2-n_1}{r}-\frac{n_2}{i}\\ p=\frac{n_1}{\frac{n_2-n_1}{r}-\frac{n_2}{i}}\end{array}$

Substituting the given values

$$\begin{gathered} p=\frac{1.0}{{\displaystyle \frac{1.5-1.0}{+30}}-{\displaystyle \frac{1.5}{+600}}} \\ p=+70.58≈71cm \end{gathered}$$

Therefore, the object distance p is +71 cm.

(c)

The radius of curvature is given in the problem, r = +30 cm.

Therefore, the radius of curvature r of the surface is +30 cm.

(d)

The image distance is given in the problem, i = +600 cm.

Therefore, the image distance i is +600 cm.

(e)

Since i < 0, the image is real and inverted.

Therefore, the image is real and inverted.

(f)

For spherical refracting surfaces, real images form on the opposite side of the object and virtual images form on the same side as the object.

Since the image is real, therefore theimage is on theoppositeside as that of the object.

Therefore, the image is on the opposite side of the object.

The required quantities can be found by using the relation between the index of refraction of object and image, image distance, object distance, and the radius of curvature.