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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Geometrical Optics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Geometrical Optics

A light ray strikes a clean slab of ice of thickness 1.00 m at an...

A light ray strikes a clean slab of ice of thickness 1.00 m1.00 \text{ m} at an angle of 45^{}^{{}^{\circ}} to the surface. It is then refracted into the ice at an angle of 30^{}^{{}^{\circ}}. Determine the time taken by the light ray to cross the slab. The speed of light in vacuum is 3×108 m s−13 \times 10^8 \text{ m s}^{-1}.

Options

  1. A4.71×10−9 s4.71 \times 10^{-9} \text{ s}
  2. B3.85×10−9 s3.85 \times 10^{-9} \text{ s}
  3. C3.33×10−9 s3.33 \times 10^{-9} \text{ s}
  4. D5.44×10−9 s5.44 \times 10^{-9} \text{ s}

Correct answer

D. 5.44×10−9 s5.44 \times 10^{-9} \text{ s}

Step-by-step solution

Angle of incidence, i = 90^{}^{{}^{\circ}} - 45^{}^{{}^{\circ}} = 45^{}^{{}^{\circ}}

Angle of refraction, r = 30^{}^{{}^{\circ}}

Refractive index of ice, \mu = \dfrac{\sin i}{\sin r} = \dfrac{\sin 45^{}^{{}^{\circ}}}{\sin 30^{}^{{}^{\circ}}} = \dfrac{1/\sqrt{2}}{1/2} = \sqrt{2}

Speed of light in ice, v=cμ=3×1082 m s−1v = \dfrac{c}{\mu} = \dfrac{3 \times 10^8}{\sqrt{2}} \text{ m s}^{-1}

Distance travelled by light in the slab, L = \dfrac{d}{\cos r} = \dfrac{1}{\cos 30^{}^{{}^{\circ}}} = \dfrac{2}{\sqrt{3}} \text{ m}

Time taken, t=Lv=2/33×108/2=2233×10−8 st = \dfrac{L}{v} = \dfrac{2 / \sqrt{3}}{3 \times 10^8 / \sqrt{2}} = \dfrac{2\sqrt{2}}{3\sqrt{3}} \times 10^{-8} \text{ s}

t=2×1.4143×1.732×10−8 s≈5.44×10−9 st = \dfrac{2 \times 1.414}{3 \times 1.732} \times 10^{-8} \text{ s} \approx 5.44 \times 10^{-9} \text{ s}
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