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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

In a double slit interference experiment, a source emits light of...

In a double slit interference experiment, a source emits light of wavelengths 480 nm480 \text{ nm} and 600 nm600 \text{ nm}. The separation between the slits is 0.25 mm0.25 \text{ mm}, and the interference is observed on a screen placed at 150 cm150 \text{ cm} from the slits. Determine the linear separation between the first maximum (adjacent to the central maximum) corresponding to the two wavelengths.

Options

  1. A0.72 mm0.72 \text{ mm}
  2. B0.36 mm0.36 \text{ mm}
  3. C1.44 mm1.44 \text{ mm}
  4. D7.2 mm7.2 \text{ mm}

Correct answer

A. 0.72 mm0.72 \text{ mm}

Step-by-step solution

The position of the nn-th maximum in a double slit interference pattern is given by yn=nλDdy_n = \dfrac{n \lambda D}{d}.

For the first maximum adjacent to the central maximum, n=1n = 1. The position is y=λDdy = \dfrac{\lambda D}{d}.

The linear separation between the first maxima corresponding to the two wavelengths λ1\lambda_1 and λ2\lambda_2 is:

Δy=y2−y1=(λ2−λ1)Dd\Delta y = y_2 - y_1 = \dfrac{(\lambda_2 - \lambda_1) D}{d}

Given values are:

λ1=480 nm=480×10−9 m\lambda_1 = 480 \text{ nm} = 480 \times 10^{-9} \text{ m}

λ2=600 nm=600×10−9 m\lambda_2 = 600 \text{ nm} = 600 \times 10^{-9} \text{ m}

D=150 cm=1.5 mD = 150 \text{ cm} = 1.5 \text{ m}

d=0.25 mm=0.25×10−3 md = 0.25 \text{ mm} = 0.25 \times 10^{-3} \text{ m}

Substituting these values into the expression for Δy\Delta y:

Δy=(600−480)×10−9×1.50.25×10−3\Delta y = \dfrac{(600 - 480) \times 10^{-9} \times 1.5}{0.25 \times 10^{-3}}

Δy=120×10−9×1.50.25×10−3\Delta y = \dfrac{120 \times 10^{-9} \times 1.5}{0.25 \times 10^{-3}}

Δy=180×10−90.25×10−3\Delta y = \dfrac{180 \times 10^{-9}}{0.25 \times 10^{-3}}

Δy=720×10−6 m\Delta y = 720 \times 10^{-6} \text{ m}

Δy=0.72×10−3 m=0.72 mm\Delta y = 0.72 \times 10^{-3} \text{ m} = 0.72 \text{ mm}
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