Matric Physics: Geometrical Optics, questions with answers

Answer: D. 42.2°

sin θc = 1/n = 1/1.49 = 0.671 ⇒ θc ≈ 42.2°.

Answer: C. ∠i > ∠c

Light must go from denser to rarer medium with angle of incidence greater than the critical angle.

Answer: A. Equal to angle of reflection

∠i = ∠r, and both rays and the normal lie in the same plane.

Answer: D. 60°

By the law of reflection, angle of incidence = angle of reflection = 60°.

Refractive index of a medium is the ratio of the speed of light in vacuum (air) to the speed of light in that medium: n = c/v. (Also n = sin i/sin r — Snell's law.) It has no unit.
n = (3 × 10⁸)/(2 × 10⁸) = 1.5

Magnifying power is the ratio of the angle subtended at the eye by the image to the angle subtended by the object when seen directly — it tells how many times larger the image appears.
Resolving power is the ability of the instrument to show two closely spaced points/objects as separate (to reveal fine detail); it depends on the aperture and the wavelength of light, not on magnification.
The near point (least distance of distinct vision) of a normal eye is about 25 cm.

Sketch a rectangular glass slab. An incident ray strikes the top face at angle i to the normal, bends towards the normal inside the glass (angle of refraction r < i), travels through the slab as the refracted ray, and at the bottom face bends away from the normal, emerging at angle e = i. Label: incident ray, normals, angle of incidence i, angle of refraction r, refracted ray, emergent ray, angle of emergence e, and the lateral displacement — the emergent ray is parallel to the incident ray but shifted sideways.

Snell's law: n = sin i / sin r ⇒ sin r = sin 35°/1.55 = 0.574/1.55 = 0.370
r = sin⁻¹(0.370) ≈ 21.7°