Question

A camera with a 100 mm focal length lens is used to photograph the sun and moon. What is the height of the image of the sun on the film, given the sun is 1.40×10⁶ km in diameter and is 1.50×10⁸ km away?

a) 1.25 mm
b) 2.50 mm
c) 5.00 mm
d) 10.00 mm

Answer 1

The height of the image of the sun on the film is approximately 0.9333 mm, using the lens formula and similar triangles concept, it's closest to option (a) 1.25 mm.

Step-by-step explanation:

To calculate the height of the image of the sun on the film, we can use the lens formula which relates the object distance (o), the image distance (i), and the focal length (f) of the lens. The formula is given by 1/f = 1/o + 1/i. However, since we're dealing with astronomical distances, the object distance is much greater than the focal length of the lens, which means that the image distance will be approximately equal to the focal length (100 mm in this case).

Once we know the image distance, we can find the height of the image using the similar triangles concept. The ratio of the image height (h') to the object height (h) will be the same as the ratio of the image distance to the object distance (i/o). Thus, the equation becomes h'/h = i/o, and we can solve for h' to find the height of the image on the film. In this case, the object (the sun) has a diameter of 1.40 x 106 km, which is its height here.

Substituting the given values, we get:

• Object height h (diameter of the sun) = 1.40 x 106 km
• Object distance o (distance from the sun to the camera) = 1.50 x 108 km
• Image distance i (approximately the focal length of the lens) = 100 mm = 0.1 m

We first convert the object height to meters: 1.40 x 106 km = 1.40 x 109 m. Then we apply the formula:

h' = (i/o) * h = (0.1 m / 1.50 x 1011 m) * 1.40 x 109 m = 0.9333 mm.

The resulting value is closest to option (a) 1.25 mm, which is the approximate height of the image of the sun on the film.