Question

Suppose your 50.0 mm focal length camera lens is 51.0 mm away from the film in the camera. (a) How far away is an object that is in focus? (b) What is the height of the object if its image is 2.00 cm high?

Answer 1

Answer:(a) For an object to be in focus, the distance from the lens to the object, d_o, must be such that the lens forms a sharp image on the film located at a distance of 51.0 mm from the lens. Using the thin lens equation,

1/f = 1/d_o + 1/d_i

where f is the focal length of the lens, and d_i is the distance between the lens and the image. Since the lens forms a sharp image on the film, d_i = 51.0 mm. Solving for d_o, we get

1/50.0 mm = 1/d_o + 1/51.0 mm

d_o = 2587 mm

Therefore, the object must be 2587 mm, or 2.59 m, away from the lens for it to be in focus.

(b) Let h_o be the height of the object and h_i be the height of the image. By similar triangles, we have

h_o / d_o = h_i / d_i

Solving for h_o, we get

h_o = (h_i * d_o) / d_i

Substituting the given values, we get

h_o = (2.00 cm * 2587 mm) / 51.0 mm

h_o = 101.2 cm

Therefore, the height of the object is 101.2 cm.

Step-by-step explanation: