Solving Prisms and Images: Find Location and Size of Image

[dancergirlie]

Homework Statement

(2) For the combination of one prism and 2 lenses shown (Fig. 1), find the location and size of the final image when the object, length 1 cm, is located as shown in the figure. [Hint: Treat the prism as a mirror, but you have to take into account the image shift caused by the prism (equivalent to a glass plate of thickness 6 cm)]

Homework Equations

n1sin(theta_1)=n2sin(theta_2)
1/f_effective=1/f1 +1/f2

The Attempt at a Solution

I don't really know how to approach this at all. Since I'm supposed to treat it like a mirror, I'm guessing that the light will be fully internally reflected. Then I would probably have to do snell's law for n1=glass and n2=air. Not really sure what the incident angles would be though. Any help would be greatly appreciated!

 

[mark726]

Thank you for your post. In order to find the location and size of the final image, we will need to use the equations you have listed. First, let's consider the prism as a mirror and find the effective focal length for the combination of the prism and the lenses. We can use the equation 1/f_effective=1/f1 +1/f2, where f1 and f2 are the focal lengths of the lenses.

Next, we can use Snell's law to find the incident angles for the light passing through the prism. As you mentioned, n1sin(theta_1)=n2sin(theta_2), where n1 is the refractive index of the glass and n2 is the refractive index of air.

Once we have the incident angles, we can use the mirror equation, 1/di + 1/do = 1/f, to find the location of the final image. Here, di is the image distance, do is the object distance, and f is the effective focal length we calculated earlier.

To find the size of the final image, we can use the magnification equation, m = -di/do, where m is the magnification, di is the image distance, and do is the object distance.

I hope this helps you approach the problem. If you need further assistance, please do not hesitate to ask. Good luck with your calculations!