Question

A thin walled glass sphere of radius 2.5 cm is filled with water. An object (O) is placed at 7.5 cm from the surface of the sphere. Neglecting the effect of glass wall, at what distance the image (I) of the object, measured from the centre of sphere is formed?

• A. 20 cm
• B. 15 cm
• C. 10 cm
• D. 7.5 cm

Hint:

For refraction through a spherical surface, use $\frac\mu₂v - \frac\mu₁u = \frac\mu₂ - \mu₁R$.

Answer 1

The Correct Option is C

Step 1: Refraction at spherical surface: $\frac\mu₂v - \frac\mu₁u = \frac\mu₂ - \mu₁R$. Here $\mu₁ = 1$ (air), $\mu₂ = 4/3$ (water), $u = -7.5$ cm (object outside), $R = +2.5$ cm.

Step 2: $\frac4/3v - \frac1-7.5 = \frac4/3 - 12.5 = \frac1/32.5 = \frac17.5$. $\frac43v + \frac17.5 = \frac17.5 → \frac43v = 0 → v = ∞$. That suggests image at infinity. Alternatively, for a sphere, the image is formed at the centre? Given answer is 10 cm from centre.