Question

A slide projector needs to create a 88-cm -high image of a 2.0-cm -tall slide. The screen is 280 cm from the slide. a. What focal length does the lens need? Assume that it is a thin lens.

Answer 1

Solution:

The height of the picture on the slide is 2 cm and the projected image on the screen is 88 cm. The slide projector magnifies the small picture to the larger image on the screen.

Step 1:
We can determine the magnification (m) by the ratio of the image height (88 cm) to the object height (2 cm), thus;

m = image height / object height
m = 88 cm / 2 cm
m = 44

The magnification is 44 times, meaning the image is 44 times larger than the slide.

Step 2:
In physics, the magnification produced by a lens is also related to the ratio of the image distance (di) and object distance (do),
therefore, we can also write magnification (m) in another way, which is:

m = -di / f

where f is the focal length and di is the distance of the image, which in this case is the distance between the screen and the slide (280 cm).

Step 3:
Place the known values in the above formula. We have to solve for the focal length (f). Thus:

- f = di / m
- f = 280 cm / 44

Hence, the focal length that the lens needs is approximately -6.36 cm. The negative sign indicates that the lens is diverging in nature.