Question

A tub is filled with a transparent liquid to a height of 30.0 cm. The apparent depth of a coin lying at the bottom of the tub is found to be 16.0 cm. The speed of light in the liquid will be ______.

Options

• 1.6 × 10⁸ m s⁻¹

• 2.0 × 10⁸ m s⁻¹

• 3.0 × 10⁸ m s⁻¹

• 2.5 × 10⁸ m s⁻¹

Answer 1

A tub is filled with a transparent liquid to a height of 30.0 cm. The apparent depth of a coin lying at the bottom of the tub is found to be 16.0 cm. The speed of light in the liquid will be 1.6 × 10⁸ m s⁻¹.

Explanation:

Using the refraction formula:

n = `"Real depth"/"Apparent depth"`

= `30/16`

Since, n = `C/C_"liquid"`

= `(3.0 xx 10^8)/C_"liquid"`

`C_"liquid" = 3.0 xx 10^8/n`

= `(3.0 xx 10^8)/(30//16)`

= 1.6 × 10⁸ m/s