ncepts and calculations:

Definitions:

$ T_1 $: Time taken for light to travel from the source to the surface of the glass slab.

$ s_1 $: Distance from the source to the surface of the slab.

$ T_2 $: Time taken for light to travel through the glass slab.

$ s_2 $: Thickness of the glass slab, which is 5 cm.

$ \mu $: Refractive index of the glass, which is 1.6.

Equating times:

We know that $ T_1 = T_2 $.

Time and velocity relationship for light:

Time is calculated as the distance divided by velocity ($\text{Time} = \frac{\text{Distance}}{\text{Velocity}}$).

For the first part of the journey, light travels from the source to the slab in a vacuum or air with speed $ c $ (speed of light in air or vacuum).

For the second part, it travels through the slab with speed $ v $, where $ v = \frac{c}{\mu} $.

Calculations:

From the equation of times:

$ \frac{s_1}{c} = \frac{s_2}{v} $

Substitute $ v = \frac{c}{\mu} $ into the equation:

$ \frac{s_1}{c} = \frac{s_2 \times \mu}{c} $

Solve for $ s_1 $:

$ s_1 = s_2 \times \mu = 5 \, \text{cm} \times 1.6 = 8 \, \text{cm} $

Therefore, the distance from the source to the surface of the glass slab is 8 cm.

Ray Optics

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