A 6 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 15 cm. The distance of the object from the lens is 10 cm. Find the size and nature of the image formed, using the lens formula.

Sure, let's solve this step by step.

Step 1: Identify the given values. The height of the object (h1) = 6 cm The object distance (u) = -10 cm (it's negative because the object is on the opposite side of the light source) The focal length (f) = 15 cm

Step 2: Use the lens formula to find the image distance (v). The lens formula is 1/f = 1/v + 1/u. We can rearrange this to find v: 1/v = 1/f - 1/u.

Substitute the given values into the formula: 1/v = 1/15 - 1/(-10) 1/v = 1/15 + 1/10 1/v = (2 + 3) / (15 * 10) 1/v = 5/150 1/v = 1/30

So, v = 30 cm. The positive sign indicates that the image is formed on the same side as the light source.

Step 3: Use the magnification formula to find the height of the image (h2). The magnification (m) is the ratio of the height of the image to the height of the object, and it's also equal to the ratio of the image distance to the object distance: m = h2/h1 = -v/u.

Rearrange the formula to find h2: h2 = m * h1.

Substitute the given values into the formula: h2 = -v/u * h1 h2 = -30/-10 * 6 h2 = 3 * 6 h2 = 18 cm

So, the image is 18 cm tall. The positive sign indicates that the image is upright.

In conclusion, the image formed is virtual, upright, and magnified. It is 18 cm tall and located 30 cm from the lens on the same side as the light source.

To find the size and nature of the image formed by the convex lens, we can use the lens formula:

1/f = 1/v - 1/u

where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens.

Given: Height of the object (h) = 6 cm Focal length of the lens (f) = 15 cm Distance of the object from the lens (u) = 10 cm

First, let's calculate the distance of the image from the lens (v):

1/15 = 1/v - 1/10

To solve this equation, we can find the common denominator:

(10v - 15v)/(15v * 10) = (10 - 15)/(10 * 15)

Simplifying the equation:

-5v/(150v) = -5/150

Cancelling out the common factors:

-5v/150v = -1/30

Simplifying further:

-1/30 = -1/30

This means that the distance of the image from the lens (v) is 30 cm.

Now, let's calculate the size of the image (h'):

Magnification (m) = h'/h = -v/u

Substituting the given values:

m = h'/6 = -30/10

Simplifying the equation:

h'/6 = -3

Multiplying both sides by 6:

h' = -18 cm

The negative sign indicates that the image is inverted.

Therefore, the size of the image formed by the convex lens is 18 cm and it is inverted in nature.