A rectangular glass block of thickness 6.0\text{ cm} has a refractive index of 1.50. Calcu… — JAMB UTME

A rectangular glass block of thickness $6.0\text{ cm}$ has a refractive index of $1.50$ . Calculate the apparent depth, in centimeters, of a mark placed at the bottom of the block when viewed normally from above.

Answer: 4 cm

Answer

The apparent depth of the mark is

4.0\text{ cm}

The refractive index of a medium relative to air is given by the ratio of real depth to apparent depth (

n = \frac{\text{Real Depth}}{\text{Apparent Depth}}

). Substituting the given values gives

\text{Apparent Depth} = \frac{6.0\text{ cm}}{1.50} = 4.0\text{ cm}

Step-by-Step Solution

Identify the relationship between refractive index, real depth, and apparent depth for normal view

n = \frac{\text{Real Depth}}{\text{Apparent Depth}}

By definition of optical refraction when looking normally from an optically less dense medium (air) into a denser medium (glass).

Substitute the known values (

n = 1.50

\text{Real Depth} = 6.0\text{ cm}

) and solve for the apparent depth

\text{Apparent Depth} = \frac{6.0\text{ cm}}{1.50} = 4.0\text{ cm}

Dividing the real thickness by the refractive index yields the perceived (apparent) depth.

Key Concept

Real and Apparent Depth in Refraction

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