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?

10

To find out how far behind the concave lens the film should be placed, we can use the lens formula:

1/f = 1/v - 1/u

Where:
- f is the focal length of the lens
- v is the image distance (distance behind the lens where the image is formed)
- u is the object distance (distance in front of the lens where the object is placed)

For the objective lens:
f1 = +41.7 cm
u1 = 4.06 m (converted to cm)
v1 = ?

Plugging in the values into the lens formula, we have:
1/41.7 = 1/v1 - 1/406

Simplifying the equation, we get:
1/v1 = 1/41.7 + 1/406

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

1/v1 = 447.7 / 16977.2

v1 = 16977.2 / 447.7
v1 ≈ 37.91 cm

So, the image formed by the objective lens is approximately 37.91 cm behind the lens.

Now, we can move on to the concave lens. Since the concave lens is placed 36.1 cm behind the objective lens, the object distance for the concave lens is the image distance of the objective lens.

For the concave lens:
f2 = -13.9 cm
u2 = v1 = 37.91 cm
v2 = ?

Using the lens formula again:
1/f2 = 1/v2 - 1/u2

Plugging in the values:
1/-13.9 = 1/v2 - 1/37.91

Simplifying the equation:
1/v2 = -1/13.9 + 1/37.91

1/v2 = (-37.91 + 13.9) / (13.9 * 37.91)

1/v2 = -24.01 / 522.7499

v2 = 522.7499 / -24.01
v2 ≈ -21.77 cm

Therefore, the image formed by the concave lens is approximately 21.77 cm in front of the lens (negative value indicates a virtual image).

To find the distance behind the concave lens where the film should be placed, we need to calculate the distance between the lens and the image:

Distance behind concave lens = Distance behind objective lens - Image distance by concave lens
Distance behind concave lens = 36.1 cm - (-21.77 cm)
Distance behind concave lens ≈ 57.87 cm

So, the film should be placed approximately 57.87 cm behind the concave lens.

Now, to find the lateral magnification of the lens combination, we can use the formula:

m = (-v1/u1) * (v2/u2)

Plugging in the values:
m = (-37.91/406) * (-21.77/37.91)

Simplifying the equation:
m = 0.0937

Therefore, the lateral magnification of this lens combination is approximately 0.0937.