Optics: distance b/w lens & slide

[kevnm67]

Homework Statement

The picture of a tree on a 35 mm color slide is 1.7 mm high. It is to be projected onto a screen 8.0 m from the slide, and is to appear 559 mm high.
a) What focal length lens (in meters) is needed?
b) What is the distance in meters between the lens and the slide?
c) What is the magnification of the system

Homework Equations

1/f = 1/s +1/s'
m=h'/h = -s'/s

The Attempt at a Solution

A)
h=1.7m
h' = 559 x 10^-3m
s' = 8 x 10^-3m
s = ?

m = 559m/1.7m = .32882 mm
.329mm = -.008mm/s
s = -24.32 mm = -.024 meters

B) Is this just asking what the focal length is?

C) m= h'/h = .329

 

[Delphi51]

s = -24.32 mm = -.024 meters

This is the answer for b. (I didn't get the minus sign; the image is inverted so the magnification is negative, but the image is on the other side of the lens from the object so I would call the distance to the image positive.)

Part a is asking for the focal length, f.

 

[kevnm67]

This is the answer for b. (I didn't get the minus sign; the image is inverted so the magnification is negative, but the image is on the other side of the lens from the object so I would call the distance to the image positive.)

Part a is asking for the focal length, f.

Your correct, both numbers are positive, but I only solved A. How do you solve B?

 

[Delphi51]

You have solved part b! That's your s = .024 meters.
For part a, solve your first formula for f.

 

[rwisz]

/-.024 = -13.7083

I would say that the focal length lens needed is approximately 24.32 mm or 0.024 meters. This can be calculated using the thin lens equation, where 1/f = 1/s + 1/s'. In this case, s' is known to be 8 meters and h and h' can be used to find s. The distance between the lens and the slide would be 24.32 mm or 0.024 meters, which is the same as the focal length of the lens. The magnification of the system is approximately -13.7083, meaning that the image on the screen is inverted and much larger than the actual object on the slide. This can be calculated using the magnification formula, where m=h'/h=-s'/s.