Question

An object lying 100 cm inside water is viewed normally from air. If the refractive index of water is \( \frac{4}{3} \), then the apparent depth of the object is:

• A. \( 100 \text{ cm} \)
• B. \( 50 \text{ cm} \)
• C. \( 25 \text{ cm} \)
• D. \( 75 \text{ cm} \)

Hint:

When an object is viewed from a rarer to a denser medium, use the formula \( d' = \frac{d}{\mu} \) to determine the apparent depth. This concept is crucial in optics, especially for refraction problems.

Answer 1

The Correct Option is D

Step 1: Understanding the Apparent Depth Formula When an object is viewed from a rarer medium (air) into a denser medium (water), the apparent depth \( d' \) is given by: \[ d' = \frac{d}{\mu} \] where: - \( d \) is the actual depth, - \( \mu \) is the refractive index of the medium (water), - \( d' \) is the apparent depth. Step 2: Substituting the Given Values Given: \[ d = 100 \text{ cm}, \quad \mu = \frac{4}{3} \] Using the formula: \[ d' = \frac{100}{\frac{4}{3}} \] \[ d' = 100 \times \frac{3}{4} \] \[ d' = 75 \text{ cm} \] Step 3: Conclusion Thus, the apparent depth of the object is 75 cm.