Question

two illuminated point objects O₁ and O₂ are placed at a distance 24 cm from each other along the principal axis of a thin convex lens of focal length 9 cm such that images of both the objects are formed at the same position. then the respective distances of the lens from O₁ and O₂ (in cm) are

Answer 1

To find the respective distances of the lens from O₁ and O₂, we can use the lens formula. Since the images of both objects are formed at the same position, the image distances for both objects will be the same. Solving the equations simultaneously will give us the values of the respective distances of the lens from O₁ and O₂.

Step-by-step explanation:

To find the respective distances of the lens from O₁ and O₂, we can use the lens formula: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance, and u is the object distance.

Since the images of both objects are formed at the same position, the image distances for both objects will be the same.

Let's assume the distance of the lens from O₁ is x. The distance of the lens from O₂ will be 24 - x (since they are placed 24 cm apart).

Using the lens formula, we can set up the equations:

1/9 = 1/v - 1/x

1/9 = 1/v - 1/(24-x)

Since the images are formed at the same position, we can equate the image distances:

v = v

Solving the equations simultaneously, we can find the values of x and 24-x.