Question:

A converging lens with a focal length of 10 cm is used to form an image of an object placed 20 cm away from the lens.

a) Determine the position and nature of the image formed. b) Calculate the magnification of the image.

Answer:

a) To determine the position and nature of the image formed by the converging lens, we can use the lens formula:

1/f = 1/di - 1/do

Here,

• f is the focal length of the lens, which is given as 10 cm.
• di is the distance of the image from the lens, which we need to find.
• do is the distance of the object from the lens, given as 20 cm.

Plugging in the known values into the lens formula, we can solve for di:

1/10 = 1/di - 1/20

Taking the reciprocal of both sides and simplifying:

10 = di/20 - 1/20 10 = di/20 - 1/20 10 = (di - 1)/20 200 = di - 1 di = 201 cm

The calculated value of di is 201 cm, which means the image is formed 201 cm away from the lens. Since the distance of the object (20 cm) is greater than the distance of the image (201 cm), the image is formed on the opposite side of the lens and is therefore a real image.

b) The magnification (m) of the image can be calculated using the formula:

m = -di/do

Substituting the calculated value of di (201 cm) and the given value of do (20 cm) into the magnification formula:

m = -201/20 m = -10.05

The calculated magnification of the image is approximately -10.05. Since the magnitude of the magnification is greater than 1, we can conclude that the image formed by the lens is magnified and upright.

In summary: a) The image is formed 201 cm away from the lens and it is a real image. b) The magnification of the image is approximately -10.05, indicating a magnified and upright image.