Question

A glass slab of thickness 4 cm contains the same number of waves as 5 cm of water. When both are traversed by the same monochromatic light. If the refractive index of water is `(4/3)`. What is that of glass?

Options

• `5/3`

• `5/4`

• `16/15`

• 1.5

Answer 1

`underlinebb(5/3)`

Explanation:

Given, Thickness of the glass slab = 4 cm

Let the number of waves be x.

The thickness of water = 5 cm

The number of waves = x (∵ it is given in the question)

We know, wave number `y_g = x/4` and `y_w = x/5`

But, we know that refractive index (μ) ∝ `1/λ` and `1/lambda` = wave number λ

So, μ ∝ y

Now, `mu_g/mu_w = y_g/y_w`

⇒ `mu_g/mu_w = (x/4)/(x/5)`

⇒ `mu_g/mu_w = 5/4`

`mu_g = 5/4 xx mu_w`

Now, substituting the values,

`mu_g = 5/4 xx 4/3`

⇒ `mu_g = 5/3`