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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Experimental Physics

NTA Abhyas 2020 · Physics · Experimental Physics

A glass hemisphere (μ = 1.5) has a radius of curvature of 16 cm. A...

A glass hemisphere (μ=1.5)\left(\mu = \text{1.5}\right) has a radius of curvature of 1616 cm. A small object OO is located on its axis halfway between the plane and spherical surface. The distance between two images, when viewed along the axis from the sides of the hemisphere, is

A glass hemisphere (μ = 1.5) has a radius of curvature of 16 cm. A small object O is located on its axis halfway

Options

  1. A3215cm\dfrac{32}{15} \text{cm}
  2. B4815cm\dfrac{48}{15} \text{cm}
  3. C6415cm\dfrac{64}{15} \text{cm}
  4. D8015cm\dfrac{80}{15} \text{cm}

Correct answer

C. 6415cm\dfrac{64}{15} \text{cm}

Step-by-step solution

When viewed from spherical side,
1v1+32×8=12×16\dfrac{1}{v1} + \dfrac{3}{2 \times 8} = \dfrac{1}{2 \times 16}
⇒1v1=132−316=−532⇒ \dfrac{1}{v1} = \dfrac{1}{32} - \dfrac{3}{16} = \dfrac{- 5}{32}
Image position is 325cm\dfrac{32}{5}cm inside the hemisphere from its periphery.
And when viewed from plane side then image is at 163cm\dfrac{16}{3}cm inside the plane surface.
∴Δx=16−163−325=6415cm∴ \Delta x = 16 - \dfrac{16}{3} - \dfrac{32}{5} = \dfrac{64}{15}cm
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