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 need to use the lens formula and the magnification formula. Here are the steps to find the image size:
Step 1: Calculate the effective focal length (feff) of the lens system using the lens formula:
1/f1 + 1/f2 = 1/feff
1/20 + 1/(-8) = 1/feff
-1/40 = 1/feff
feff = -40 cm
Step 2: Calculate the magnification (m) of the lens system using the magnification formula:
m = -(feff / f2)
m = -(-40 / -8)
m = 5
Step 3: Calculate the object size (o) on the film plane using the formula:
o = 2 × tan(α/2) × d
where α is the subtended angle and d is the distance between the lenses.
o = 2 × tan(2∘/2) × 15
o ≈ 0.0707 cm
Step 4: Calculate the image size (i) on the film plane using the formula:
i = m × o
i ≈ 5 × 0.0707
i ≈ 0.3535 cm
Therefore, the image size on the film plane of a distant object subtending an angle of 2∘ at the camera is approximately 0.3535 cm.