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Geometrical Optics question

2023 · 11 Apr · Shift 2 · Q61
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  5. /2023 · 11 Apr · Shift 2 · Q61

Geometrical Optics question

2023 · 11 Apr · Shift 2 · Q61

JEE MainPhysicsGeometrical OpticsNumerical+4 / −1
As shown in the figure, a plane mirror is fixed at a height of 50 cm50 \mathrm{~cm}50 cm from the bottom of tank containing water (μ=43)\left(\mu=\frac{4}{3}\right)(μ=34​). The height of water in the tank is 8 cm8 \mathrm{~cm}8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ‾cm\underline{\hspace{2cm}}\mathrm{cm}​cm. JEE Main 2023 (Online) 11th April Evening Shift Physics - Geometrical Optics Question 75 English
Numerical answer
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Correct answer: 98

  1. Understand the setup
  • Bottom of tank contains a small bulb.
  • Water height = 8 cm8\,\text{cm}8cm.
  • A plane mirror is fixed at a height of 50 cm50\,\text{cm}50cm from the bottom.
  • Refractive index of water: μ=43\mu = \dfrac{4}{3}μ=34​.

So, between the bulb and mirror:

  • first 8 cm8\,\text{cm}8cm is water,
  • remaining 50−8=42 cm50-8=42\,\text{cm}50−8=42cm is air.
  1. Apparent depth of bulb as seen from air

For an object inside water viewed from air, the apparent depth is

apparent depth=real depthμ\text{apparent depth} = \frac{\text{real depth}}{\mu}apparent depth=μreal depth​

Thus the bulb at real depth 8 cm8\,\text{cm}8cm appears to be at depth

84/3=8×34=6 cm\frac{8}{4/3} = 8\times \frac{3}{4} = 6\,\text{cm}4/38​=8×43​=6cm

below the water surface.

  1. Position of apparent object relative to mirror

The water surface is 8 cm8\,\text{cm}8cm above the bottom, so the apparent position of the bulb is

8−6=2 cm8 - 6 = 2\,\text{cm}8−6=2cm

above the bottom of the tank.

The mirror is at 50 cm50\,\text{cm}50cm above the bottom, so the distance of this apparent object from the mirror is

50−2=48 cm50 - 2 = 48\,\text{cm}50−2=48cm
  1. Image formed by plane mirror

A plane mirror forms image at the same distance behind the mirror as the object is in front of it.

Hence the image will be 48 cm48\,\text{cm}48cm behind the mirror.

Therefore, distance of image from bottom of tank is

50+48=98 cm50 + 48 = 98\,\text{cm}50+48=98cm
  1. Final answer
98 cm\boxed{98\,\text{cm}}98cm​
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