Question

An air bubble in water ($ \mu = \frac{4}{3} $) is shown in the figure. The apparent depth of the image of the bubble in a plane mirror viewed by the observer is.

• A. 16 cm
• B. 18 cm
• C. 24 cm
• D. 12 cm

Hint:

When calculating the apparent depth of an object submerged in a medium, use the formula \( \frac{\text{Real depth}}{\mu} \), where \( \mu \) is the refractive index of the medium.

Answer 1

The Correct Option is C

The apparent depth of an object in a medium is given by the formula: \[ \text{Apparent depth} = \frac{\text{Real depth}}{\mu} \] where \( \mu \) is the refractive index of the medium. For the bubble in water, the real depth is the sum of the depth of the bubble (8 cm) and the distance from the surface to the bubble (24 cm), giving a total real depth of 24 cm. 
Since the refractive index of water is \( \mu = \frac{4}{3} \), the apparent depth of the image in the plane mirror will be: \[ \text{Apparent depth} = \frac{24}{\frac{4}{3}} = 24 \, \text{cm} \] 
Thus, the apparent depth of the image is 24 cm.