Question

The lens equation is (1/f)=(1/p)+(1/q), where f is the focal length of the lens, p is the distance of the object from the lens, and q is the distance of the image from the lens. What is the distance of an object from a lens if the image of the object is 20 millimeters from the lens, and the focal length of the lens is 16 millimeters?

a) 32 mm
b) 12.8 mm
c) 8 mm
d) 40 mm

Answer 1

To find the distance of an object from the lens when the image is 20 millimeters away and the focal length of the lens is 16 millimeters, we can use the lens equation (1/f) = (1/p) + (1/q). Rearranging this equation and substituting the given values, we can solve for p to determine the object distance. The result is a distance of 8 millimeters.

Step-by-step explanation:

To find the distance of an object from the lens, we can rearrange the lens equation (1/f) = (1/p) + (1/q) to solve for p. Given that the image distance (q) is 20 millimeters and the focal length (f) is 16 millimeters, we substitute these values into the equation.

(1/16) = (1/p) + (1/20)

To solve for 1/p, we multiply both sides of the equation by 16p and simplify:

p + (16p/20) = 16

Then, we combine like terms:

(20p + 16p)/20 = 16。

We can simplify further to get:

36p/20 = 16

Finally, we solve for p by multiplying both sides of the equation by 20/36 and simplifying:

p = (20/36) x 16 = 8 millimeters。