Question 1

Two coherent light sources of wavelength 500 nm produce an interference pattern. If the path difference at a point is 1500 nm, how many wavelengths does this path difference represent?

Accepted Answer

Number of wavelengths = Path difference / Wavelength = 1500 nm / 500 nm = 3.

Question 2

A monochromatic light of wavelength 600 nm passes through a single slit of width 0.3 mm. What is the order of the first dark fringe in single slit diffraction?

Accepted Answer

In single slit diffraction, dark fringes occur at a sin θ = m λ where m = 1, 2, 3... for first, second, third dark fringes respectively.

Question 3

In a diffraction grating experiment, light of wavelength 550 nm is incident normally. The second order maximum occurs at an angle of 30°. What is the grating spacing (distance between adjacent slits)?

Accepted Answer

Using grating equation d sin θ = m λ, we get d = m λ / sin θ = (2 × 550 × 10⁻⁹) / sin 30° = (1100 × 10⁻⁹) / 0.5 = 2.2 μm.

Question 4

Light of frequency 6 × 10¹⁴ Hz passes through a medium of refractive index 1.5. What is the wavelength of light in the medium? (Speed of light = 3 × 10⁸ m/s)

Accepted Answer

Wavelength in medium λₘ = (c/n)/f = (3×10⁸/1.5)/(6×10¹⁴) = (2×10⁸)/(6×10¹⁴) = 333 nm ≈ 300 nm.

Question 5

In Young's double slit experiment, the distance between two slits is 1 mm, and they are illuminated with light of wavelength 650 nm. The distance to the screen is 1 m. What is the fringe width?

Accepted Answer

Fringe width β = λD/d = (650 × 10⁻⁹ × 1) / (1 × 10⁻³) = 0.65 × 10⁻³ m = 0.65 mm.

Question 6

In Young's double slit setup, if the slit separation is halved while keeping wavelength and screen distance constant, the fringe width becomes:

Accepted Answer

Fringe width β = λD/d; if d is halved, β is doubled.

Question 7

A diffraction grating has 2000 lines per cm. What is the grating spacing (d)?

Accepted Answer

Grating spacing d = 1/N = 1/2000 cm = 5 × 10⁻⁵ cm.

Question 8

In a diffraction grating experiment, light of wavelength 480 nm produces a second-order maximum at angle 60°. What is the grating spacing?

Accepted Answer

Using d sin θ = nλ; d × sin(60°) = 2 × 480×10⁻⁹; d = (960×10⁻⁹)/(√3/2) ≈ 1.1 μm.

Question 9

Two incoherent light sources of equal intensity I₀ are superposed. What is the resultant intensity?

Accepted Answer

For incoherent sources, intensities add directly: I_total = I₀ + I₀ = 2I₀.

Question 10

A diffraction pattern from a single slit shows the central maximum width of 4 mm on a screen 1.5 m away. If the wavelength is 600 nm, what is the slit width?

Accepted Answer

Central maximum width = 2λD/a; 4×10⁻³ = (2 × 600×10⁻⁹ × 1.5)/a; a = 0.45 mm.

Question 11

Two coherent light sources of wavelength 600 nm are separated by a distance of 3 mm. They are placed in front of a screen at a distance of 2 m. What is the fringe width in the interference pattern?

Accepted Answer

Fringe width β = λD/d = (600×10⁻⁹ × 2)/(3×10⁻³) = 0.4 mm.

Question 12

In Young's double slit experiment, the distance between the first minima and the central maxima is 2 mm. If the wavelength is 500 nm and the distance to screen is 1 m, what is the slit separation?

Accepted Answer

Distance to first minima = λD/(2d), so 2×10⁻³ = (500×10⁻⁹ × 1)/(2d), giving d = 0.25 mm.

Question 13

A single slit of width 0.1 mm produces a diffraction pattern with the first minima at 30°. What is the wavelength of light used?

Accepted Answer

For single slit minima: a sin θ = nλ; (0.1×10⁻³) × sin(30°) = 1 × λ; λ = 500 nm.

Question 14

Two light waves of amplitudes A₁ = 4 units and A₂ = 3 units interfere constructively. What is the resultant amplitude?

Accepted Answer

For constructive interference, resultant amplitude = A₁ + A₂ = 4 + 3 = 7 units.

Question 15

In a diffraction grating experiment, light of wavelength 400 nm is incident normally. If the grating has 5000 lines per cm, what is the grating spacing?

Accepted Answer

Grating spacing d = 1/(number of lines per unit length) = 1/(5000 × 10² m⁻¹) = 2.0 × 10⁻⁶ m.

Question 16

When monochromatic light of wavelength 550 nm passes through a single slit of width 0.11 mm, the first minimum occurs at an angle of 30°. Which statement is correct according to single slit diffraction?

Accepted Answer

For single slit diffraction, the first minimum occurs when a sin θ = λ, which is the definition of the first dark fringe.

Question 17

In Young's double slit experiment, the distance between two slits is 0.5 mm, the distance to the screen is 1 m, and the wavelength of light is 500 nm. Calculate the fringe width.

Accepted Answer

Fringe width β = λD/d = (500 × 10⁻⁹ × 1)/(0.5 × 10⁻³) = 1.0 × 10⁻³ m = 1.0 mm.

Question 18

Two coherent light sources of wavelength 600 nm produce an interference pattern. If the path difference between two points on the screen is 1800 nm, how many wavelengths of path difference exist?

Accepted Answer

Path difference = 1800 nm; number of wavelengths = 1800/600 = 3 wavelengths.

Agniveer Army Technical Wave Optics

Wave Optics — Practice Questions