Angular Spread Of Blue and Red Light Through Plastic

[fs93]

Homework Statement

The index of refraction for blue light in plastic is 1.46 and for red light is 1.39. Determine the angular spread of the spectrum leaving the plastic block [presumably to air] for a beam of white light incident at angle of 45° to the plastic block.

Homework Equations

n1/n2=sinI/sinR

The Attempt at a Solution

They are asking for white light, but I am only given blue and red?
Using Snell's law to find:

Blue - 1.46/1=sin45/sinX
sinX=0.48
X= 28.97

Red - 1.39/1=sin45/sinY
sinY=0.52
Y=31.33

Is that right? Would blue would leave at 28.97° and red at 31.33°. What about white light?

Thanks.

 

[kuruman]

What wavelength is white light?

 

[tomcue]

Yes, your calculations for the angles of blue and red light leaving the plastic block are correct. However, for white light, you would need to consider the entire spectrum of colors, not just blue and red. This means that the angular spread of white light would be the range of angles between which the different colors (wavelengths) of light would leave the plastic block.

To calculate this, you could use the equation n1/n2=sinI/sinR for each color of light, and then find the difference between the maximum and minimum angles. Alternatively, you could use the relationship between the index of refraction and the wavelength of light, given by n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium (in this case, plastic). This would allow you to calculate the angle of refraction for each color of light and then find the difference between the maximum and minimum angles.

Overall, the angular spread of white light through the plastic block would depend on the specific wavelengths present in the white light beam, as well as the index of refraction for each of those wavelengths in the plastic.