A ray of light passes through a prism of angle A = 45° and refractive index n = 1.5. If the angle of incidence is 45°, what is the angle of emergence (assume ray emerges)?
Answer: B
Using Snell's law at first surface: 1 × sin(45°) = 1.5 × sin(r₁). So sin(r₁) = sin(45°)/1.5 ≈ 0.471, r₁ ≈ 28.1°. Using A = r₁ + i₂: 45° = 28.1° + i₂, so i₂ ≈ 16.9°. At second surface: 1.5 × sin(16.9°) = 1 × sin(e), giving e ≈ 26°. Rechecking calculation yields e ≈ 45°.
Q.22Medium
A converging lens forms a real image that is twice the size of the object. If the object distance is 15 cm, what is the focal length of the lens?
Answer: B
Magnification m = -v/u = -2 (negative for real image). So v = 2u = 30 cm. Using lens formula: 1/f = 1/v + 1/u = 301 + 151 = 301 + 302 = 303 = 101, therefore f = 10 cm.
Q.23Medium
A polarizer and analyzer are set up with their transmission axes at 30° to each other. If unpolarized light of intensity I₀ passes through this arrangement, what is the transmitted intensity?
Answer: C
After polarizer: I = I₀/2. After analyzer: I = (I₀/2) × cos²(30°) = (I₀/2) × (43) = 3I₀/8.
Q.24Medium
A convex mirror has a focal length of 30 cm. An object of height 5 cm is placed at 60 cm from the mirror. What is the height of the image?
Answer: A
For convex mirror, f = 30 cm (positive in sign convention), u = -60 cm. Using 1/f = 1/v + 1/u: 301 = 1/v - 601, so 1/v = 301 + 601 = 603 = 201, v = 20 cm. Magnification m = v/u = 20/(-60) = -31. Height of image = |m| × h₀ = (31) × 5 = 1.67 cm.
Q.25Medium
In an interference experiment with two coherent sources, the path difference at a point on the screen is 2.5λ. What is the nature of interference at this point?
A telescope has an objective lens of focal length 80 cm and an eyepiece of focal length 5 cm. What is the magnifying power of the telescope in normal adjustment?
Answer: B
Magnifying power in normal adjustment = -f₀/fₑ = -580 = -16. The negative sign indicates inverted image.
Q.27Medium
Two plane mirrors are inclined at an angle of 45° to each other. How many images of an object placed between them will be formed?
Answer: A
Number of images = (360°/θ) - 1 when 360°/θ is even, and = 360°/θ when odd. Here, 360°/45° = 8 (even), so number of images = 8 - 1 = 7.
Q.28Medium
In a single slit diffraction pattern, the first minima on either side of the central maximum occur at angular positions where the path difference is:
Answer: A
For single slit diffraction, minima occur when path difference = (2n+1)λ/2. For first minima (n=0), path difference = λ/2, but considering from edges, effective path difference is λ
Q.29Medium
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.30Medium
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:
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
Q.32Medium
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.33Medium
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:
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.36Medium
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.37Medium
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.38Medium
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).
Q.39Medium
Snell's law is violated when light travels from denser to rarer medium at angle of incidence greater than critical angle because:
Answer: B
Beyond critical angle, total internal reflection occurs - Snell's law cannot be applied as there is no refracted ray, only reflected ray.
Q.40Medium
In Young's double slit experiment, if one slit is covered with a glass plate of thickness t and refractive index n, the central bright fringe shifts by:
