Question

if an object is kept 20 cm away from the lens and the image is formed 40 cm away from the lens then what is the focal length of the lens and what type of lens it is?find the magnification also

Answer 1

Given : An object is kept 20cm away from the lens and the image is formed 40 cm away from the lens.

To find : The focal length of the lens, Type of lens and The magnification of lens.

solution : here u = -20 cm

v = 40 cm

we know, for concave lens, magnitude of magnification is always less than 1.

but here, m = v/u = 40/20 = 2 > 1

so, lens is definitely converging. i.e., convex lens.

using formula, 1/v - 1/u = 1/f

⇒1/40 - 1/-20 = 1/f

⇒1/40 + 1/20 = 1/f

⇒f = 40/3 ≈ 13.3 cm

focal length of lens is 13.3 cm (approximately).

magnification of lens , m = v/u = 40/-20 = -2

negative sign indicates that image is real.

Answer 2

Focal length of lens = 13.33 cm

Convex lens

Magnification = 2

Explanation:

Given: Object distance u = 20cm. Image distance v = 40

Find: Focal length f of the lens, type of lens and magnification m.

Solution:

m = v / u = 40 / 20 = 2.

Since m is greater than 1, the lens is convex lens.

To find f, we can use the formula 1/v - 1/u = 1/f

1/40 - 1/-20 = 1/f

1/40 + 1/20 = 1/f

 (2 + 1) / 40 = 1/f

So f = 40/3 = 13.33 cm