Red and blue light enter together into a glass plate of 10 cm. what is the distance between red and blue light whenthe light emerges from the plate. n(blue) = 1.6, n(red) = 1.3

The distance between the emergent red and blue light is 3 cm

Solution:

As per the question:

Thickness of the glass plate, s = 10 cm = 0.1 m

Refractive index of blue light,

Refractive index of blue light,

Now, to calculate the distance between red and blue light as it emerges from the plate:

We know that refractive index is given as the ratio of speed of light in vacuum, c or air to that in medium, .

           (1)

Since, c is constant, thus

n ∝

Now, the refractive index of blue light is more than that of red light thus its speed in medium is lesser than red light.

Now, time taken, t by red and blue light to emerge out of the glass slab:

In the same time, red light also traveled through the glass covering some distance in air say x

         (2)

Time taken by red light to cover 'x' distance in vacuum is t'':

Now,

t = t' + t"           (3)

From eqn (1), (2) and (3):

Now, putting appropriate values in the above eqn:

x = 0.03 m = 3 cm

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000

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