Question

An object is at a distance 25 cm from the
curved surface of a glass hemisphere of radius
10 cm. Find the position of the image (u = 1.5)
(1) 93.3 cm(2) 80 cm
(3) 100 cm
(4) 85 cm​

Answer 1

Answer:

1)93.3 cm is the answer I think

Answer 2

The position of the image is at 100 cm

Therefore, option (3) is correct.

Explanation:

Given:

Distance of the object u = 25 cm

Refractive index of spherical glass $\mu_2$ = 1.5

Radius of the glass hemisphere R = 10 cm

To find out:

The position of the image

Solution:

If the distance of the image is v

Then using the refraction formula for spherical surface

$\frac{\mu_2}{v}+\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R}$

$\frac{1.5}{v}+\frac{1}{25}=\frac{1.5-1}{10}$

$\implies \frac{1.5}{v}+\frac{1}{25}=\frac{1}{20}$

$\implies \frac{1.5}{v}=\frac{1}{20}-\frac{1}{25}$

$\implies \frac{1.5}{v}=\frac{5-4}{100}$

$\implies \frac{1.5}{v}=\frac{1}{100}$

$\implies \frac{1}{v}=\frac{1}{150}$

$\implies v=150$ cm

The apparent distance of image formed

$d'=\frac{v}{\mu}$

$\implies d'=\frac{150}{1.5}$

$\implies d'=100$ cm

Hope this answer is helpful.

Know More:

Q: An object is placed at a distance of 10cm from the curved surface of a glass hemisphere of radius 10cm. Find the position of the image from the flat surface .

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