A simple camera telephoto lens consists of two lenses. The objective lens has a focal length f1 = +41.7 cm. Precisely 36.1 cm behind this lens is a concave lens with a focal length f2 = -13.9 cm. The object to be photographed is 4.06 m in front of the objective lens. How far behind the concave lens should the film be placed?

What is the lateral magnification of this lens combination?

To find the distance behind the concave lens where the film should be placed, we can use the lens formula:

1/f = 1/v - 1/u

Where f is the focal length, v is the image distance, and u is the object distance.

For the objective lens:

f1 = +41.7 cm
u1 = 4.06 m = 406 cm
v1 = ?

Plugging these values into the lens formula:

1/41.7 = 1/v1 - 1/406

To solve for v1, we rearrange the equation:

1/v1 = 1/41.7 + 1/406

1/v1 = (406 + 41.7)/(41.7 * 406)

v1 = (41.7 * 406)/(406 + 41.7)

v1 ≈ 40.72 cm

Now, for the concave lens:

f2 = -13.9 cm
u2 = v1 = 40.72 cm
v2 = ?

Using the same lens formula:

1/-13.9 = 1/v2 - 1/40.72

1/v2 = 1/-13.9 + 1/40.72

v2 = (40.72 * -13.9)/(40.72 - (-13.9))

v2 ≈ -18.67 cm

Since the image formed by the concave lens is virtual (negative image distance), it means that we have to place the film behind the lens. Therefore, the distance behind the concave lens where the film should be placed is approximately 18.67 cm.

To find the lateral magnification, we can use the following formula:

m = -v1/v2

Plugging in the values:

m = -40.72/-18.67

m ≈ 2.18

Therefore, the lateral magnification of this lens combination is approximately 2.18.