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JEE Main 2013 (25 Apr, Shift 1) · Refraction, Glass Slab & Apparent Depth

Refraction, Glass Slab & Apparent Depth question from JEE Main 2013 (25 Apr, Shift 1)

Q72JEE Main 2013 · 25 APR · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

A printed page is pressed by a glass of water. The refractive index of the glass and water is 1.5 and 1.33, respectively. If the thickness of the bottom of glass is 1 cm and depth of water is 5 cm, how much the page will appear to be shifted if viewed from the top?

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Answer:

  1. Normal shift by a layer: s=t(1−1μ)s = t\left(1 - \frac{1}{\mu}\right); shifts of layers add.
  2. Glass: s1=1(1−11.5)=0.333 cms_1 = 1\left(1 - \frac{1}{1.5}\right) = 0.333\text{ cm}
  3. Water: s2=5(1−11.33)=5×0.248=1.241 cms_2 = 5\left(1 - \frac{1}{1.33}\right) = 5 \times 0.248 = 1.241\text{ cm}
  4. Total shift =0.333+1.241≈1.57 cm= 0.333 + 1.241 \approx 1.57\text{ cm}.
  5. This value is not among the options; the answer usually quoted for this question is (c) 1.3533 cm1.3533\text{ cm}.
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