1. A convex lens is held over a piece of paper outdoors on a sunny day. When the

Question

1. A convex lens is held over a piece of paper outdoors on a sunny day. When the paper is held 26 cm below the lens, the sunlight is focused on the paper and the paper ignites. What is the focal length of the lens?

2. A lens for a 35-mm camera has a focal length given by f=55mm. (a) How close to the film should the lens be placed to form a sharp image of an object that is 5.0m away? (b) what is the magnification of the image on the film?

3. Albert is nearsighted, and without his eyeglasses he can focus only on objects less than 2.2m away. (a) Are Albert's eyeglasses concave or convex? Explain. (b) To correct Alberts's nearsightedness, his eyeglasses must produce a virtual, upright image at a distance of 2.2 m when viewing an infinitely distant object. What is the focal length of Albert's eyeglasses?

Explanation / Answer

1)

The focal length is the distance from the lens where parallel rays entering the lens
all converge to the same point.

The sun is so far away its rays are essentially
parallel, so they will converge at the focal length. So the focal length is 26 cm.
In the formula 1/di + 1/do = 1/f, di is the distance of the image and do the distance
of the object,

in this case the sun. Here, the distance of
the sun is so great that the term 1/do is essentially zero, and can be ignored.
The formula then becomes 1/di + 0 = 1/f so di = f, which in this case is 26 cm.

So, f = 26 cm

2)

If v is the distance in mm:
1 / 5000 + 1 / v = 1 / 55
v = 1 / 55 - 1 / 5000
v= 17.9 mm.

(b)
If m is the magnification:
m = 17.9/ 5000
m= 0.00359

3)

Convex since virtual, upright image is formed

f = 2.2 m

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