Question

Learning Goal: To become familiar with using the image of one instrument as the object of the next and tracing rays through a system of multiple instruments. Multiple optics refers to any system of more than one optical instrument through which light passes. Most devices related to optics, such as cameras, microscopes, and telescopes, contain multiple optics systems. In multiple optics, the image of one optical instrument becomes the object of the next one. Thus, in multiple optics problems, you need to find the image created by the first optical instrument that the rays encounter. Then, you will use that image as the object of the next optical instrument, repeating this pattern until you have followed the rays all the way through the system. It is very important to be alert to the geometry and to signs when you find the object distance for one instrument from the location of the previous instrument's image. Sometimes, the image is formed on the virtual side of the instrument, leading to a virtual object. This may sound strange, but in practice, its effect on your calculations is simply to make the object distance negative instead of positive. Several optical instruments are placed along the x axis, with their axes aligned along the x axis. A plane mirror is located at x=0. A converging lens with focal length 5.00 m is located at x=12.5m. An object is placed at x=22.5m. Next, find the location of the image created by the plane mirror (after the light has passed through the lens).

In order to find the location of the final image of the object formed by this system, you will need to trace the rays through the system, instrument by instrument. You are strongly advised to draw a picture with the x axis and the location of the lens, mirror, and object marked. Then, as you proceed through the problem, you can mark where each image is located.

Part A

First, find the location of the image created by the lens by itself (as if no other instruments were present).

Express your answer in meters, to three significant figures, or as a fraction.

Part B

Next, find the location of the image created by the plane mirror (after the light has passed through the lens).

Express your answer in meters, to three significant figures, or as a fraction.

Answer 1

Object distance

s= 22.5 m – 12.5 m = 10 m.

We have

1/f=1/s+1/s'

1/5=1/10+1/s'

s'=10 m

Location of the image is 12.5m-10 m= 2.50 m

b)

for plane mirror

s=2.5 m

for plane mirror f=0

1/0=1/2.5 +1/s'

s'=-2.50m