Optics- Total internal reflection

[johndoe]

A small source of light at the bottom face of a rectangular glass slab 2.25 cm thick is viewed from above. Rays of light totally internally reflected at the top of the surface outline a circle of 7.6cm in diameter in the bottom surface. Determine the refraction index of the glass.

This is what I interpreted:

I can find out the angle of incidence and reflection (theta 1), but then I am stuck. please help.

 

[Redbelly98]

My understanding is that the light source is at the bottom. Light is emitted, strikes the top surface where it is reflected at some angle, and returns to the bottom surface. The light source and 7.6 cm circle are both at the bottom surface.

The words "viewed from above" seem misleading and irrelevant.

 

[kerimek]

Hello,

Thank you for sharing your question. Based on the provided information, we can use the formula for total internal reflection to determine the refractive index of the glass.

The formula is: n = sin(theta 2) / sin(theta 1)

In this case, theta 1 is the angle of incidence, which is equal to the angle of reflection since the light is totally internally reflected. This means that theta 1 = theta 2.

We also know that the diameter of the circle formed by the reflected rays is 7.6 cm. Using basic geometry, we can calculate that the radius of the circle is 3.8 cm.

Now, we can use the formula for the critical angle of total internal reflection to calculate theta 1 (or theta 2). The formula is: sin(theta c) = n2 /n1, where n1 is the refractive index of air (assumed to be 1) and n2 is the refractive index of the glass.

Since we know that the angle of incidence and reflection are the same, we can substitute theta 1 for theta c and solve for n2:

sin(theta 1) = n2 / 1
sin(theta 1) = n2

We can use the inverse sine function to find the value of theta 1:
theta 1 = sin^-1 (3.8/2.25)
theta 1 = 58.4 degrees

Now we can substitute this value for theta 1 in the original formula to solve for n2:

n = sin(theta 2) / sin(theta 1)
n = sin(58.4) / sin(58.4)
n = 1

This means that the refractive index of the glass is equal to 1, which is the same as air. This may seem surprising, but it is possible if the glass slab is made of a material with a very low refractive index, such as fused silica or crown glass.

I hope this helps to answer your question. Please let me know if you need any further clarification or assistance.

Best,