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Question
A spherical surface of radius 30 cm separates two transparent media A and B with refractive indices 1.33 and 1.48 respectively. The medium A is on the convex side of the surface. Where should a point object be placed in medium A so that the paraxial rays become parallel after refraction at the surface?
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Solution
Given,
Spherical surface of radius (R) = 30 cm
Medium A has refractive index (μ1) = 1.33
Medium B has refractive index (μ2) = 1.48
Medium A is the convex side of surface.
Since,
We know that paraxial rays become parallel after refraction
i.e, the image of the point object will be formed at infinity.
Therefore v = ∞
Using the lens equation,
\[\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}\]
\[ \Rightarrow \frac{1 . 48}{\infty} - \frac{1 . 33}{u} = \frac{1 . 48 - 1 . 33}{30}\]
\[ \Rightarrow - \frac{1 . 33}{u} - \frac{0 . 15}{30}\]
\[ \therefore u = - 266 . 0 cm\]
Hence, the object is placed at a distance of 266.0 cm from the convex surface on side A.
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