Question

A convex lens of focal length 20cm is placed at a distance of 80cm from a wall. How far from
the wall an object must be placed such that the image is formed on the wall?​

Answer 1

Answer:

The object should be placed at a distance of 80/3 cm from the lens.

Step-by-step explanation:

Let the wall be at the right side of the lens. Let the left side of the lens be negative and right side positive. So, we are given these values:

Focal length of a convex lens is positive, since the light rays after passing through the lens meet at the other side of the lens.

Focal length of lens (f) = +20cm

The image needs to be obtained on the wall, which is on the right side of the lens.

Distance of image (v) = +80cm

Distance of object from the lens (u) = ?

Applying the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ we get:

$\frac{1}{20} = \frac{1}{80} - \frac{1}{u}$

⇒ $\frac{1}{u} = \frac{1}{80} - \frac{1}{20} = -\frac{3}{80}$

⇒ $u = -\frac{80}{3}$

Since the distance is negative, the object should be placed at the left side of the lens (according to the above-mentioned sign convention).