A thin lens has power +5 diopters. Find its focal length.
Answer: A
Power P = 1/f. f = 51 = 0.2 m = 20 cm. Positive power indicates convex lens.
Q.182Easy
A ray of light travels from medium 1 (refractive index n₁ = 1.5) to medium 2 (refractive index n₂ = 1.0). If the angle of incidence is 30°, what is the angle of refraction?
Answer: A
Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂). So 1.5 × sin(30°) = 1.0 × sin(θ₂). This gives sin(θ₂) = 0.75, therefore θ₂ = 48.6°
Q.183Easy
A concave mirror produces a real, inverted, and magnified image. Where is the object located?
Answer: A
For a concave mirror, when object is between F and C, the image is real, inverted, and magnified. This is the magnification region used in shaving mirrors.
Q.184Easy
In a single-slit Fraunhofer diffraction pattern, the first minimum occurs at angle θ. At what angle does the second minimum occur?
Answer: B
For single-slit diffraction, minima occur at positions where a·sin(θ) = mλ, where m = 1, 2, 3... Since sin is approximately proportional to θ for small angles, the second minimum occurs at approximately 2θ.
Q.185Easy
A plano-convex lens (n = 1.5) has radius of curvature R for the curved surface. What is its focal length?
Answer: B
Using lens maker's formula: 1/f = (n-1)[1/R₁ - 1/R₂]. For plano-convex: 1/f = (1.5-1)[1/R - 1/∞] = 0.5/R. Therefore f = 2R.
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Q.186Easy
Two coherent sources of light have a phase difference of π/2 radians. What is the nature of interference at their meeting point?
Answer: C
For constructive interference, phase difference = 0, 2π, etc. For destructive interference, phase difference = π, 3π, etc. Phase difference of π/2 gives partial or incomplete interference with intermediate intensity.
Q.187Easy
A plane mirror is moved towards a stationary object at a distance of 10 cm from the mirror. What is the velocity of the image if the mirror moves with a velocity of 2 m/s towards the object?
Answer: A
When a plane mirror moves towards an object with velocity v, the image also moves towards the mirror with velocity v. The relative velocity of approach between object and image is 2v. Therefore, velocity of image = 2 × 2 = 4 m/s.
Q.188Easy
A concave lens of focal length 20 cm forms an image at a distance of 10 cm from the lens. At what distance from the lens should the object be placed?
Answer: B
Using lens formula: 1/f = 1/v + 1/u. For concave lens, f = -20 cm, v = -10 cm (virtual image). So 1/-20 = 1/-10 + 1/u gives 1/u = -201 + 101 = 201, therefore u = 20 cm.
Q.189Easy
In Young's double slit experiment, the distance between slits is 0.5 mm, distance to screen is 1 m, and wavelength is 500 nm. What is the fringe width?
A light ray undergoes refraction from medium 1 (n₁ = 1.33) to medium 2 (n₂ = 1.5). If the angle of incidence is 30°, what is the angle of refraction?
Answer: B
Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂). So 1.33 × sin(30°) = 1.5 × sin(θ₂). Therefore 1.33 × 0.5 = 1.5 × sin(θ₂), which gives sin(θ₂) = 0.443, θ₂ ≈ 27.8°.
Q.191Easy
The critical angle for total internal reflection from a denser medium to air (n = 1) is 45°. What is the refractive index of the denser medium?
Answer: A
At critical angle: sin(θc) = 1/n. So sin(45°) = 1/n gives 1/√2 = 1/n, therefore n = √2 ≈ 1.41.
Q.192Easy
In a diffraction grating with 5000 lines per cm, what is the grating constant (distance between adjacent slits)?
Answer: A
Grating constant d = 1/(number of lines per unit length) = 50001 cm⁻¹ = 2.0 × 10⁻⁴ cm or 2 μm.
Q.193Easy
In a laser experiment, the wavelength of light is 632.8 nm. What is the frequency of this light? (Take c = 3 × 10⁸ m/s)
Answer: A
Frequency f = c/λ = (3 × 10⁸)/(632.8 × 10⁻⁹) = (3 × 10⁸)/(6.328 × 10⁻⁷) ≈ 4.74 × 10¹⁴ Hz.
Q.194Easy
A light ray travels from medium A (refractive index 1.5) to medium B (refractive index 1.0). If the angle of incidence is 30°, what is the angle of refraction?
