Related Problems with Solution

Problem 3 : A converging lens with a focal length of 15 cm forms a real image 30 cm from the lens. Calculate the object distance and the height of the object if the image is twice the size of the object.#

Solution :#

Use the lens formula: 1/f = 1/v + 1/u

• f = focal length of the lens = 15 cm
• v = image distance = 30 cm
• Let h be the height of the object and 2h be the height of the image.

Plugging these values into the formula: 1/15 = 1/30 - 1/u

Now, solve for u: 1/u = 1/15 - 1/30 1/u = (2 - 1)/30 1/u = 1/30

u = 30 cm

Now that we have the object distance (u), we can calculate the height of the image (h’) using the magnification formula: Magnification (M) = -v/u = (2h)/h -30/30 = -1 Solve for h: -1 = -2