How is a rainbow formed (Figure 1) ? Recall that the index of refraction of a me
ID: 1520121 • Letter: H
Question
How is a rainbow formed (Figure 1) ? Recall that the index of refraction of a medium is slightly different for different colors. When white light from the Sun enters a spherical raindrop, as shown in (Figure 2) , the light is refracted or bent. After reflecting off the back surface of the drop, the light is refracted again as it leaves the front surface. Each drop separates the colors of light. An observer on the ground with her back to the Sun sees at most one color of light coming from a particular drop (see (Figure 3) ). If the observer sees red light from a drop (for example, the top drop in (Figure 3) ), the violet light for that same drop is deflected above her head. However, if she sees violet light coming from a drop lower in the sky, the red light from that drop is deflected below her eyes onto the ground. She sees red light when her line of view makes an angle of 42 with the beam of sunlight and violet light when the angle is 40. Other colors of light are seen at intermediate angles. Part A Suppose that light entered one side of a square water droplet of refractive index 1.33 at an incident angle of 21 . Some of the light reflects off the back surface and then goes back out on the same side as it entered. Find the angle of refraction of light leaving the square droplet. Express your answer using two significant figures.
Explanation / Answer
How is a rainbow formed (Figure 1) ?
Recall that the index of refraction of a medium is slightly different for different colors.
When white light from the Sun enters a spherical raindrop, as shown in (Figure 2) ,
the light is refracted or bent.
After reflecting off the back surface of the drop, the light is refracted again as it leaves the front surface.
Each drop separates the colors of light.
An observer on the ground with her back to the Sun sees at most one color of light coming from a particular drop (see (Figure 3) ).
If the observer sees red light from a drop (for example, the top drop in (Figure 3) ),
the violet light for that same drop is deflected above her head.
However,
if she sees violet light coming from a drop lower in the sky, the red light from that drop is deflected below her eyes onto the ground.
She sees red light when her line of view makes an angle of 42 with the beam of sunlight and violet light when the angle is 40. Other colors of light are seen at intermediate angles.
Part A
Suppose that light entered one side of a square water droplet of refractive index 1.33 at an incident angle of 21 .
Some of the light reflects off the back surface and then goes back out on the same side as it entered.
Find the angle of refraction of light leaving the square droplet.
Express your answer using two significant figures.
Here,
index of refraction of air, n1 = 1
index of refraction of water, n2 = 1.33
angle of incidence, Ai = 21 degrees
From Snells law,
n1*SinAi = n2*SinAr
Solving for angle of refraction,
Ar = arcSin((n1/n2)*SinAi)
Ar = arcSin((1/1.33)*Sin21)
Ar = 15.632 degrees or 16 degrees( two sig fgures)