A Young's double slit apparatus features slits separated by 0.28 mm and a screen located 48 cm from the slits. The entire setup is submerged in water, and the slits are illuminated with red light ( λ = 700 nm in

Correct answer: A. 0.9 mm Given: d = 0.28 mm = 0.28 × 10^ -3 m D = 48 cm = 0.48 m λ = 700 nm = 700 × 10^ -9 m The refractive index of water is μ = (4)/(3) . The wavelength of light in water is given by: λ' = (λ)/(μ) = 700 × 10^ -9 (4)/(3) = 525 × 10^ -9 m The fringe-width is given by the formula: β = (λ' D)/(d) Substituting the values: β = 525 × 10^ -9 × 0.48 0.28 × 10^ -3 β = 525 × 10^ -6 × (48)/(28) β = 525 × 10^ -6 × (12)/(7) β = 75 × 12 × 10^ -6 m β = 900 × 10^ -6 m = 0.9 mm

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Light Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Light Waves

A Young's double slit apparatus features slits separated by 0.28 mm...

A Young's double slit apparatus features slits separated by

0.28 \text{ mm}

and a screen located

48 \text{ cm}

from the slits. The entire setup is submerged in water, and the slits are illuminated with red light (

\lambda = 700 \text{ nm}

in vacuum). Determine the fringe-width of the pattern produced on the screen.

Options

A $0.9 \text{ mm}$
B $1.2 \text{ mm}$
C $0.8 \text{ mm}$
D $1.6 \text{ mm}$

Correct answer

A. $0.9 \text{ mm}$

Step-by-step solution

Given:

d = 0.28 \text{ mm} = 0.28 \times 10^{-3} \text{ m}

D = 48 \text{ cm} = 0.48 \text{ m}

\lambda = 700 \text{ nm} = 700 \times 10^{-9} \text{ m}

The refractive index of water is

\mu = \dfrac{4}{3}

.

The wavelength of light in water is given by:

\lambda' = \dfrac{\lambda}{\mu} = \dfrac{700 \times 10^{-9}}{\dfrac{4}{3}} = 525 \times 10^{-9} \text{ m}

The fringe-width is given by the formula:

\beta = \dfrac{\lambda' D}{d}

Substituting the values:

\beta = \dfrac{525 \times 10^{-9} \times 0.48}{0.28 \times 10^{-3}}

\beta = 525 \times 10^{-6} \times \dfrac{48}{28}

\beta = 525 \times 10^{-6} \times \dfrac{12}{7}

\beta = 75 \times 12 \times 10^{-6} \text{ m}

\beta = 900 \times 10^{-6} \text{ m} = 0.9 \text{ mm}

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