Question

A light 5 cm high is placed 54 cm in front of a converging lens with a focal length of 20 cm. Use GRASP to calculate the image distance and image height. Round your final answers to integers (no decimal places). Describe the image using SALT.

Options:
A) Image distance: 30 cm, Image height: 2 cm
B) Image distance: 40 cm, Image height: 3 cm
C) Image distance: 50 cm, Image height: 4 cm
D) Image distance: 60 cm, Image height: 5 cm

Answer 1

The image distance is 32 cm and the image height is 32 cm.

Step-by-step explanation:

To calculate the image distance and image height, 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, and u is the object distance.

Given that the object distance (u) is 54 cm, the focal length (f) is 20 cm, and the height of the object is 5 cm. Plugging these values into the lens formula, we can solve for the image distance D and image height H:

D = (u)/(u-f) = (20 cm*54 cm) / (54 cm - 20 cm) = 1080 cm / 34 cm = 31.8 cm ≈ 32 cm

H = (D/d) * h = (32 cm / 5 cm) * 5 cm = 32 cm, rounded to integers.

So, the correct option is A) Image distance: 30 cm, Image height: 2 cm.