A light ray falling at an angle of 60 ∘ with the surface of a clean slab of ice of thickness 1.00 m is refracted into it at an angle of 15 ∘ . Calculate the time taken by the light rays to cross the slab. Speed of light in vacuum = 3×10 8 m/s

To solve this problem, we need to use Snell's law and the formula for speed, distance, and time.

1. First, we need to find the refractive index of ice. We can use Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocity of light in the first medium to the velocity in the second medium, or the refractive index.

   So, n = sin(i) / sin(r) = sin(60) / sin(15)

2. Calculate the above expression to find the refractive index of ice.

3. Next, we need to find the speed of light in ice. We can use the formula c = c0 / n, where c0 is the speed of light in vacuum and n is the refractive index.

4. Calculate the speed of light in ice using the refractive index from step 2.

5. Now, we need to find the actual path of the light in the ice. The light doesn't go straight down, but at an angle. So, the path length d can be found using the formula d = thickness / cos(r), where r is the angle of refraction.

6. Calculate the path length using the thickness of the ice slab and the angle of refraction.

7. Finally, we can find the time it takes for the light to cross the slab using the formula t = d / c, where d is the path length and c is the speed of light in ice.

8. Calculate the time using the path length from step 6 and the speed of light from step 4.

This will give you the time taken by the light rays to cross the slab.