Find the size, nature and position of the image formed when an object of 1.5cm size is formed at a distance of 15cm from a concave mirror of focal length 10cm?

Question

Answer

Answer

Concave Mirror Image Formation

Given:

Object size (h) = 1.5 cm

Object distance (u) = -15 cm

Focal length (f) = -10 cm (negative for concave mirror)

Formula:

The formula for finding the image distance (v) using object distance (u) and focal length (f) is:

1/f = 1/v + 1/u

The formula for finding the magnification (m) is:

m = -v/u

Where:

v = image distance

u = object distance

f = focal length

m = magnification

Solution:

Given values are:

h = 1.5 cm

u = -15 cm

f = -10 cm

Using the formula, we can find the image distance:

1/f = 1/v + 1/u

1/-10 = 1/v + 1/-15

-3v/2 = -1

v = 2/3 x 15 = 10 cm

The image distance is 10 cm.

Now, we can find the magnification:

m = -v/u

m = -10/-15

m = 2/3

The magnification is 2/3.

We can also find the size and nature of the image:

The image size is given by:

h' = m x h

h' = 2/3 x 1.5

h' = 1 cm

The image size is 1 cm.

The nature of the image can be found using the magnification:

If m is positive, the image is erect.

If m is negative, the image is inverted.

Since m is negative, the image is inverted.

The image is inverted and 1 cm in size.

Conclusion:

An object of size 1.5 cm placed at a distance of 15 cm from a concave mirror of focal length 10 cm forms an inverted image of size 1 cm at a distance of 10 cm from the mirror.

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