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Geometrical Optics question

2016 · 10 Apr · Shift 1 · Q48
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Geometrical Optics question

2016 · 10 Apr · Shift 1 · Q48

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are :
  1. A
    Two
  2. B
    Three
  3. C
    Four
  4. D
    Five
View written solutionFree

Correct answer: B

  1. Principle used

To determine the refractive index μ\muμ of a glass slab using a travelling microscope, we use

μ=real thicknessapparent thickness.\mu = \frac{\text{real thickness}}{\text{apparent thickness}}.μ=apparent thicknessreal thickness​.

So we need:

  • the real thickness of the slab,
  • the apparent thickness of the slab.
  1. How these are measured with a travelling microscope

Let the microscope reading for the top surface of the slab be R1R_1R1​.

Let the reading for the bottom surface seen through the slab be R2R_2R2​.

Then the apparent thickness is

ta=∣R1−R2∣.t_a = |R_1 - R_2|.ta​=∣R1​−R2​∣.

Now, to get the real thickness, we need one more reading. After removing the slab, focus on the mark/needle/base corresponding to the bottom position and take reading R3R_3R3​.

Then the real thickness is

tr=∣R1−R3∣.t_r = |R_1 - R_3|.tr​=∣R1​−R3​∣.

Hence,

μ=trta=∣R1−R3∣∣R1−R2∣.\mu = \frac{t_r}{t_a} = \frac{|R_1 - R_3|}{|R_1 - R_2|}.μ=ta​tr​​=∣R1​−R2​∣∣R1​−R3​∣​.
  1. Minimum number of readings

Thus, the minimum readings required are:

  1. Reading of top surface,
  2. Reading of bottom surface as seen through slab,
  3. Reading of bottom position after removing slab.

So the minimum number of readings = 3.

  1. Option check
  • A: Two — not sufficient, because both real and apparent thickness cannot be obtained.
  • B: Three — correct.
  • C: Four — not minimum.
  • D: Five — not minimum.

Therefore, the correct answer is

B: Three\boxed{\text{B: Three}}B: Three​
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