A lens has power +5 D. A second lens of power -2 D is placed in contact with it. The equivalent focal length of the combination is:
Answer: A
Power combination: P = P₁ + P₂ = 5 + (-2) = 3 D. Focal length f = 1/P = 31 = 0.33 m
Q.542Medium
A monochromatic light source produces a diffraction pattern using a diffraction grating. If the wavelength is decreased, the diffraction angle for the first order maximum will:
Answer: A
Using grating equation: d×sin(θ) = mλ. For fixed m and d, if λ decreases, sin(θ) decreases, hence θ decreases
Q.543Medium
An air bubble of radius 2 mm is formed in water (refractive index 1.33). The critical angle for light traveling from water to air is approximately:
In a compound microscope, the objective has focal length 0.5 cm and eyepiece has focal length 5 cm. If the least distance of distinct vision is 25 cm, the magnifying power is:
Answer: C
Magnifying power m = (v₁/u₁) × (D/fe) ≈ -(L/fo) × (D/fe) = (025.5) × (525) = 50 × 5 = 250. With proper calculation considering tube length, result is approximately 1250
Q.545Medium
When unpolarized light of intensity I₀ passes through two polarizers whose transmission axes are at 60° to each other, the final intensity is:
Answer: A
After first polarizer: I = I₀/2. After second polarizer (at 60°): I = (I₀/2)cos²(60°) = (I₀/2)(41) = I₀/8
Advertisement
Q.546Easy
The refractive index of a material is found to be 1.5. The speed of light in this material is:
Answer: B
n = c/v. 1.5 = (3 × 10⁸)/v. v = (3 × 10⁸)/1.5 = 2 × 10⁸ m/s
Q.547Hard
In a fiber optics cable, light undergoes total internal reflection. The minimum refractive index of the core material needed to guide light from air is:
Answer: C
For total internal reflection at core-cladding boundary: n_core × sin(θc) = n_cladding × 1. For propagation at 45°, n_core ≥ √2 ≈ 1.414
Q.548Medium
An object is at a distance of 20 cm from a convex lens of focal length 15 cm. The nature of the image formed is:
Answer: A
Using lens formula: 1/f = 1/u + 1/v. 151 = 201 + 1/v. v = 60 cm (positive, real image). Since u < 2f, magnification |m| = 2060 = 3 > 1 (magnified)
Q.549Medium
Coherent light from a laser (λ = 632.8 nm) is used in Young's double slit experiment. The distance between slits is 0.5 mm and screen distance is 1 m. The fringe width is:
When light passes through a glass slab of thickness t and refractive index n, the lateral displacement is maximum when the angle of incidence is:
Answer: D
Lateral displacement d = t × sin(i - r)/cos(r). Displacement is maximum when ∂d/∂i = 0, which occurs approximately at high incident angles, practically around 60°
Q.551Medium
The equivalent focal length of two lenses in contact is 10 cm. If the focal lengths are 15 cm and f₂, then f₂ is:
An astronomical telescope in normal adjustment has objective focal length 100 cm and eyepiece focal length 5 cm. The magnifying power is:
Answer: B
Magnifying power m = -f₀/fe = -5100 = -20 (negative sign indicates inverted image)
Q.553Hard
In Brewster's angle incidence, the reflected and refracted rays are:
Answer: B
At Brewster's angle θB, tan(θB) = n₂/n₁. The reflected ray and refracted ray are perpendicular (θB + (90° - θr) = 90°)
Q.554Hard
A thin air gap of thickness d is created between two glass plates. For constructive interference in reflected light with wavelength λ, the condition is:
Answer: A
For air gap with phase change at one surface, constructive interference occurs when 2d = mλ (accounting for the phase change of π at reflection from denser medium)
Q.555Medium
The resolving power of a telescope is inversely proportional to:
Answer: D
Resolving power ∝ 1/θ_min where θ_min = 1.22λ/D. So resolving power ∝ D/λ, inversely proportional to both wavelength and inversely related to aperture diameter
Q.556Easy
A plane mirror is moved towards a stationary object at a speed of 5 m/s. The speed at which the image approaches the object is:
Answer: B
When mirror moves towards object at speed v, the image also moves towards object at speed v. Therefore, relative speed = v + v = 2v = 10 m/s
Q.557Easy
Light of wavelength 500 nm in vacuum enters a medium of refractive index 1.5. The wavelength in the medium is:
Answer: A
Wavelength in medium = λ_vacuum / n = 1500.5 = 333.3 nm. Frequency remains constant in different media.
Q.558Easy
A concave mirror of focal length 20 cm forms a real, inverted, and magnified image. The object must be placed:
Answer: C
For magnified real image in concave mirror, object distance u must be between f and 2f (between focus and center of curvature), giving magnification m > 1.
Q.559Medium
Two coherent sources emit light of wavelength λ. If path difference is 2.5λ, the interference will be:
Answer: B
For destructive interference, path difference = (2n+1)λ/2. Here 2.5λ = 5λ/2 = (2×2+1)λ/2, which is destructive.
Q.560Medium
A convex lens of focal length 30 cm is used as a magnifying glass. For maximum magnification, the object should be placed:
Answer: C
For magnifying glass (virtual image), object is placed between f and lens. Maximum magnification occurs when final image is at least distance of distinct vision (25 cm).
