CBSE 2025 · Region 7 · Set 3 · Q30 · 4 marks

When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $\displaystyle 90^{\circ}$ is called the critical angle ( $\displaystyle \mathrm{i}_{\mathrm{c}}$ ) for the given pair of media. This angle is related to the refractive index of medium $\displaystyle 1$ with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.

(i)

An object is placed in front of a convex spherical glass surface ( $\displaystyle \mathrm{n}=1.5$ and radius of curvature R ) at a distance of $\displaystyle 4$ R from it. As the object is moved slowly close to the surface, the image formed is :

(A)

always real

(B)

always virtual

(C)

first real and then virtual

(D)

first virtual and then real

(ii)

A double-convex lens, made of glass of refractive index $\displaystyle 1 \cdot 5$, has focal length $\displaystyle 10$ cm . The radius of curvature of its each face, is :

(A)

$\displaystyle 10$ cm

(B)

$\displaystyle 15$ cm

(C)

$\displaystyle 20$ cm

(D)

$\displaystyle 40$ cm

(iii)

A small bulb is placed at the bottom of a tank containing a transparent liquid (refractive index n ) to a depth H . The radius of the circular area of the surface of liquid, through which light from the bulb can emerge out, is $\displaystyle R$. Then $\displaystyle \left(\frac{R}{H}\right)$ is :

(A)

$\displaystyle \frac{1}{\sqrt{\mathrm{n}^{2}-1}}$

(B)

$\displaystyle \sqrt{\mathrm{n}^{2}-1}$

(C)

$\displaystyle \frac{1}{\sqrt{\mathrm{n}^{2}+1}}$

(D)

$\displaystyle \sqrt{\mathrm{n}^{2}+1}$

(iv)

(a)OR(b)

A parallel beam of light is incident on a face of a prism with refracting angle $\displaystyle 60^{\circ}$. The angle of minimum deviation is found to be $\displaystyle 30^{\circ}$. The refractive index of the material of the prism is close to :

(A)

$\displaystyle 1 \cdot 3$

(B)

$\displaystyle 1 \cdot 4$

(C)

$\displaystyle 1 \cdot 5$

(D)

1.$\displaystyle 6$

CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.