An object is placed at a distance of 30 cm from a convex lens of focal length 20 cm. Find the position of the image.

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

1/f = 1/v - 1/u

Where: f = focal length of the lens v = distance of the image from the lens u = distance of the object from the lens

Given: f = 20 cm u = -30 cm (negative sign indicates that the object is placed on the same side as the incident light)

Substituting the given values into the lens formula, we have:

1/20 = 1/v - 1/-30

Simplifying the equation, we get:

1/20 = 1/v + 1/30

To solve for v, we can find the common denominator:

1/20 = (3 + 2)/60

1/20 = 5/60

Now, we can equate the numerators:

1 = 5v/60

Cross-multiplying, we have:

60 = 5v

Dividing both sides by 5, we get:

v = 12 cm

Therefore, the position of the image formed by the convex lens is 12 cm from the lens.

Sure, we can use the lens formula to solve this problem. The lens formula is given by:

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.

Given in the problem: f = 20 cm (convex lens so focal length is positive) u = -30 cm (object is on the same side as the light source, so distance is negative)

Substituting these values into the lens formula gives:

1/20 = 1/v - (-1/30)

Solving this equation for v gives:

1/v = 1/20 + 1/30

To add these fractions, find a common denominator, which is 60:

1/v = 3/60 + 2/60

Adding these fractions gives:

1/v = 5/60

Solving for v gives:

v = 60/5

So, v = 12 cm.

Therefore, the image is formed 12 cm on the other side of the lens from where the object is placed.