A negative lens with a focal length of -10.0 cm is on the same axis as a positive lens with a focal length of +20.0 cm as illustrated. The distance between the lenses is 20.0 cm. A real object 3.00 cm high is placed 20.0 cm to the left of the negative lens. After the light has passed through both lenses, the image is
A) 3.0 cm high and virtual.
B) 1.0 cm high and virtual.
C) 1.0 cm high and real.
D) 3.0 cm high and real.
E) None of these is correct.

Question

A negative lens with a focal length of -10.0 cm is on the same axis as a positive lens with a focal length of +20.0 cm as illustrated. The distance between the lenses is 20.0 cm. A real object 3.00 cm high is placed 20.0 cm to the left of the negative lens. After the light has passed through both lenses, the image is
A) 3.0 cm high and virtual. 
B) 1.0 cm high and virtual. 
C) 1.0 cm high and real. 
D) 3.0 cm high and real. 
E) None of these is correct.

Quizplus · Accepted Answer

First, we need to use the thin lens equation to find the distance between the negative lens and the image.

1/f = 1/di - 1/do

For the negative lens, f = -10 cm and do = -20 cm (since the object is to the left of the lens). Solving for di, we get:

1/-10 = 1/di - 1/-20 
-1/10 = 1/di + 1/20 
-1/10 - 1/20 = 1/di 
-3/20 = 1/di 
di = -6.67 cm

So the image formed by the negative lens is 6.67 cm to the left of the negative lens.

Now we need to use the thin lens equation again to find the final image distance and height. For the positive lens, f = 20 cm and do = 6.67 cm (since the image from the negative lens is the new object for the positive lens). Solving for di, we get:

1/20 = 1/di - 1/6.67 
1/20 + 1/6.67 = 1/di 
di = 4.44 cm

Finally, we can use the magnification equation to find the height of the final image:

m = hi/ho = -di/do 
m = (-4.44 cm)/(20.0 cm) = -0.222

Since the magnification is negative, the image is inverted. And since the magnification is less than one, the image is smaller than the object.

hi = m*ho = (-0.222)*(3.00 cm) = -0.666 cm ≈ 1.0 cm

So the final image is 1.0 cm high and real (since it is formed on the opposite side of the positive lens from the object).

A Negative Lens with a Focal Length of -10