CBSE Class 12 Physics Optics Solved Examples

CBSE Class 12 Physics Optics Solved Examples. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

Ex.1 A person looking through the telescope T just sees the point A on the rim at the bottom of a cylindrical vessel when the vessel is empty. When the vessel is completely filled with a liquid of refractive index 1.5, he observes a mark at the centre B, of the bottom, without moving the telescope or the vessel. What is the height of the vessel if the diameter of its cross-section is 10 cm. ?
Sol.: The vessel is filled with liquid of refractive index μ when the ray from B reaches the telescope.

Ex.2 A parallel beam of light rays is incident on a transparent sphere of radius R and index of refraction μ in the direction of one of the diameters. At what distance from the centre of the sphere will the rays be focussed? Assume that μ < 2.
Sol.: For refractional first surface μ₁ =1,μ2 =μ, μ =-∞, v=? r=+R

   μ/v - 1/ ∞=   μ-1/R → v=  μR/ μ-1

For refraction at second surface:

I′ serves as object for the second surface. Now μ₁ = μ (since light is going from sphere to air) and  μ₂= μ
   u= BI'= +( μR/ μ-1 -2R) = R(2- μ)/ μ-1

(It is the positive  because light is travelling  from left to right and the  distance is also from left to right.)

v=?, r=-R

1/v- μ( μ-1)/R( μ-1)=1- μ/-R or v = R(2- μ)/2( μ-1)

This distance is positive and is refered from the second surface.
∴ distance of the focal point from the centre

Ex.3 A hollow sphere of glass of refractive index μ has a small mark on its interior surface which is observed from a point outside the sphere on the side opposite the centre. The inner cavity in concentric with the external surface and the thickness of the glass is uniform and equal to the radius of the inner surface. Prove that the mark will appear nearer than it really is by a distance (μ-1)R /(3μ-1) where R is theradius of the inner surface.

Sol.: For the refraction at surface I

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