Question

An object is placed at 30 cm in front of a convex lens of focal length 20 cm. Find the position of the image. What is the magnification of the object? ​

Answer 1

To determine the position of the image and the magnification of the object, we can use the thin lens equation, which relates the distance of the object (u), the distance of the image (v), and the focal length of the lens (f).

The thin lens equation is given by:

1/f = 1/v - 1/u

where f is the focal length, v is the distance of the image from the lens, and u is the distance of the object from the lens.

Given that the object is placed at a distance of 30 cm from a convex lens of focal length 20 cm, we can substitute the given values into the thin lens equation.

1/20 = 1/v - 1/30

Simplifying the equation, we get:

1/v = 1/20 + 1/30

1/v = 1/12

v = 12 cm

Therefore, the position of the image is 12 cm from the lens.

To determine the magnification of the object, we can use the magnification equation, which relates the height of the image (h_i) and the height of the object (h_o).

The magnification equation is given by:

m = -v/u = h_i/h_o

where m is the magnification, v is the distance of the image from the lens, u is the distance of the object from the lens, h_i is the height of the image, and h_o is the height of the object.

Given that the object is at a distance of 30 cm from the lens, we can substitute the given values into the magnification equation.

m = -12/30

m = -0.4

Therefore, the magnification of the object is -0.4, which indicates that the image is inverted and smaller than the object.

Answer 2

=> To find the position of the image formed by a convex lens and the magnification of the object, we can use the lens formula and magnification formula.

Given:

• Object distance (u) = -30 cm (negative sign indicates object is in front of the lens)
• Focal length (f) = 20 cm

Position of the Image:

The lens formula states:

1/f = 1/v - 1/u

Substituting the given values:

1/20 = 1/v - 1/-30

Simplifying:

1/20 = (30 - v)/(-30v)

Cross-multiplying:

20(-30v) = (30 - v)

-600v = 30 - v

Combining like terms:

-599v = 30

Dividing both sides by -599:

v ≈ -0.05 cm

——>The position of the image formed by the convex lens is approximately -0.05 cm.

Magnification of the Object:

The magnification (m) is given by the formula:

m = -v/u

Substituting the values:

m = -(-0.05 cm)/(-30 cm)

m ≈ 0.00167

——>The magnification of the object is

approximately 0.00167.

• ■ The positive value indicates that the image is upright compared to the object.

Hope this helps u :)