A 5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length  20 cm. The distance of the object from the lens is 30 cm.  Find the magnification of the image formed.

Sure, here is the step by step solution:

Step 1: Identify the given values: Object height (h1) = 5 cm Focal length (f) = 20 cm Object distance (u) = -30 cm (The object is always placed on the left side of the lens, so the distance is taken as negative)

Step 2: Use the lens formula to find the image distance (v): 1/f = 1/v + 1/u Rearrange the formula to solve for v: 1/v = 1/f - 1/u Substitute the given values into the formula: 1/v = 1/20 - 1/(-30) 1/v = 1/20 + 1/30 1/v = (3 + 2) / 60 1/v = 5/60 v = 60/5 v = 12 cm

Step 3: Use the magnification formula to find the magnification (m): m = -v/u Substitute the given values into the formula: m = -12/-30 m = 0.4

So, the magnification of the image formed by the lens is 0.4. This means the image is 0.4 times the size of the object, or in other words, the image is smaller than the object.

To find the magnification of the image formed by the convex lens, we can use the formula:

magnification (m) = - (image distance / object distance)

Given: Object height (h) = 5 cm Focal length (f) = 20 cm Object distance (u) = 30 cm

First, we need to find the image distance (v) using the lens formula:

1/f = 1/v - 1/u

Substituting the given values: 1/20 = 1/v - 1/30

Simplifying the equation: 1/v = 1/20 + 1/30 1/v = (3 + 2) / 60 1/v = 5/60 v = 60/5 v = 12 cm

Now, we can calculate the magnification using the formula:

m = - (v / u)

Substituting the values: m = - (12 / 30) m = - 0.4

Therefore, the magnification of the image formed by the convex lens is -0.4.