Optics Problem: Duplicating Newton's Results with Lens and Prism

[MJPause]

We wish to attempt to duplicate some of Newton's results with a lens and prism. A lens with focal length 10cm is placed in a ray of sunlight, and a prism is placed at the "downstream" focal point of the lens. The light passing through the prism is broken into its component colors. If it is an equilateral prism (all of the prism angles are 60 degrees), made of crown glass (n=1.52), and the light is incident at a 30 degree angle to one face of the prism:

a. how far from the lens is the prism placed?
b. what is the angle of deviation for light (greenish yellow) of wavelength 589 nm?
c. what angle of incidence is required for total internal reflection within the prism?

I have no idea how to start or do this problem. HELP!

 

[cupid.callin]

and a prism is placed at the "downstream" focal point of the lens.

what does this statement means>?

 

[MJPause]

If f (which is the distance from the focal point to the lens) is positive, then the "upstream" focus is on the side of the incoming light and the "downstream" focus is on the side of the ongoing light.

 

[cupid.callin]

so for a
you already specified that prism is at downstream focal point ...

 

[rwisz]

I would first like to commend you for attempting to replicate Newton's results and using a lens and prism to do so. This is a great way to understand and appreciate the work of past scientists.

To answer your questions, we can use the laws of refraction and Snell's law to calculate the necessary parameters. Let's break down the problem step by step.

a. To determine the distance between the lens and prism, we can use the lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. Since the focal length is given as 10cm, we can plug that in and solve for u. Assuming that the image distance is the distance between the lens and the prism, we can get u = 10cm.

b. Now, to find the angle of deviation for greenish yellow light (wavelength = 589 nm), we can use the equation: θ = sin^-1[(n-1)sin(α)/n], where θ is the angle of deviation, n is the refractive index of the prism (given as 1.52), and α is the angle of incidence (given as 30 degrees). Plugging in these values, we get θ = 41.6 degrees.

c. Finally, to calculate the angle of incidence required for total internal reflection within the prism, we can use the critical angle formula: θc = sin^-1(n2/n1), where n1 is the refractive index of the medium surrounding the prism (air, with a value of 1) and n2 is the refractive index of the prism (1.52). Plugging in these values, we get θc = 42.4 degrees.

I hope this helps you understand how to approach and solve this problem. Remember, as a scientist, it's important to always use the laws and principles of physics to solve problems and replicate experiments. Keep up the good work!