Question

How do your results from ray tracing compare to your results from using the thin-lens equation?

What is the focal length of a convex lens that produces an image 10 cm away with a magnification of -0.5? Show all calculations in your answer.
Hint: Use the definition of magnification and the thin-lens equation.

Answer 1

20cm

Step-by-step explanation:

A convex lens has a positive focal length and the object placed in front of it produce both virtual and real image (image distance can be negative or positive depending on the nature of the image).

According to the lens equation

`(1)/(f) = (1)/(u) + (1)/(v)` where;

f is the focal length of the lens

u is the object distance

v is the image distance

If the magnification is - 0.6

mag = v/u = -0.5

v = -0.5u

since v = 10cm

10 = -0.5u

u = -10/0.5

u =-20 cm

Substitute u = -20cm ( due to negative magnification)and v = 10cm into the lens formula to get the focal length f

`(1)/(f) = (1)/(u) + (1)/(v)\\(1)/(f) = (1)/(-20) + (1)/(10)\\(1)/(f) = (1)/(-20) + (1)/(10)\\(1)/(f) = (-1+2)/(20) \\(1)/(f) = (1)/(20) \\cross \ multiply\\f = 20\\f = 20 cm`

Hence the focal length of the convex lens is 20cm