Telephoto lenses allow one to "zoom in" on distant objects, making them bigger. A particular telephoto lens consists of a combination of two thin lenses having focal lengths of f1=20 cm and f2=−8 cm, respectively. The lenses are separated by a distance of d=15 cm. Determine the image size in cm on the film plane, located at the back focal point of the lens system, of a distant object subtending an angle of α=2∘ at the camera.

To determine the image size on the film plane, we can use the thin lens equation and the magnification formula.

1. Start by calculating the effective focal length (feff) of the telephoto lens system. The formula for combining thin lenses in contact is given by:

1/feff = 1/f1 + 1/f2 - d/(f1 * f2)

Substituting the given values, we have:

1/feff = 1/20 + 1/(-8) - 15/(20 * -8)

Simplifying the equation, we get:

1/feff = -2/17

Taking the reciprocal of both sides, we find:

feff = -17/2 cm

2. Next, we can calculate the magnification (M) of the lens system using the formula:

M = -(feff / f1)

Substituting the values, we get:

M = -(-17/2 / 20)
= 17/40

3. Now, let's determine the object size (h) using the given angle (α) and the formula:

h = 2 * tan(α/2) * distance to the object

Substituting the values, we have:

h = 2 * tan(2/2) * distance to the object
= 2 * tan(1) * distance to the object

Since the object is at a distant, we can assume the distance to be very large. In this case, the tangent of the angle α is approximately equal to the angle itself in radians. Thus:

h ≈ 2 * 1 * distance to the object
= 2 * distance to the object

4. Finally, let's find the image size (h') on the film plane using the magnification formula:

h' = M * h

Substituting the values, we get:

h' = (17/40) * (2 * distance to the object)
= 17/20 * distance to the object

Therefore, the image size on the film plane, located at the back focal point of the lens system, of a distant object subtending an angle of α=2∘ at the camera is approximately equal to (17/20) times the distance to the object.