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A large glass block of refractive index 1.5 contains a spherical air bubble of radius R . A point object is placed inside the glass at a distance x from the nearest surface of the bubble, on the normal to the surface. Considering refraction only at this nearest surface, a virtual image is formed at a distance x 2 from the surface. The value of x is

Options

  1. AR
  2. B4 R
  3. C7 R
  4. D2 R

Correct answer

A. R

Step-by-step solution

For refraction at a single spherical surface, the formula is: ₂ v - ₁ u = ₂ - ₁ R Here, light travels from glass to air, so the first medium is glass ( ₁ = 1.5 ) and the second medium is air ( ₂ = 1 ). The center of curvature of the bubble lies in the air, which is in the direction of the incident light, so the radius of curvature R is positive. Given: Object distance, u = -x Image distance, v = - x 2 (since the image is virtual and formed on the same side) Substituting the values into the formula: 1 - x 2 - 1.5 -x

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