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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up, to the surface of the liquid and moves along its surface (see figure). How fast is the light traveling in the liquid?

A

1.8×108 m/s1.8 \times 10^8 \text{ m/s}

B

2.4×108 m/s2.4 \times 10^8 \text{ m/s}

C

3.0×108 m/s3.0 \times 10^8 \text{ m/s}

D

1.2×108 m/s1.2 \times 10^8 \text{ m/s}

Step-by-Step Solution

  1. Identify the Phenomenon: When a ray of light moves along the surface of the liquid after travelling from a denser medium (liquid) to a rarer medium (air), the angle of refraction is 90∘90^\circ. The angle of incidence in the liquid is called the Critical Angle (ici_c).
  2. Snell's Law: μsin⁡ic=1×sin⁡90∘  ⟹  sin⁡ic=1μ\mu \sin i_c = 1 \times \sin 90^\circ \implies \sin i_c = \frac{1}{\mu}.
  3. Relation to Speed: The refractive index μ\mu is defined as the ratio of the speed of light in vacuum (cc) to the speed in the medium (vv): μ=cv\mu = \frac{c}{v} . Substituting this into the critical angle formula: sin⁡ic=vc\sin i_c = \frac{v}{c}.
  4. Calculation: From the standard geometry associated with this AIPMT 2007 problem (typically a triangle with height 4 units and base 3 units, where the ray strikes the surface), the sine of the critical angle is 332+42=35=0.6\frac{3}{\sqrt{3^2+4^2}} = \frac{3}{5} = 0.6. Using c≈3.0×108 m/sc \approx 3.0 \times 10^8 \text{ m/s} : v=c×sin⁡icv = c \times \sin i_c v=3.0×108×0.6v = 3.0 \times 10^8 \times 0.6 v=1.8×108 m/sv = 1.8 \times 10^8 \text{ m/s}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from RAY OPTICS AND OPTICAL INSTRUMENTS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSrestingbottombeakerfilledliquid

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