A concave mirror having a radius of curvature 40 cm is placed in front of an illuminated point source at a distance of 30 cm from it.Find the location of the image.

To find the location of the image, we can use the mirror formula for concave mirrors:

1/f = 1/v - 1/u

Where:
- f is the focal length of the mirror,
- v is the distance of the image from the mirror, and
- u is the distance of the object from the mirror.

Given:
- Radius of curvature (R) = 40 cm
- Distance of the object (u) = -30 cm (negative sign indicates that the object is placed in front of the mirror)

The focal length (f) of a concave mirror is half of the radius of curvature:
f = R/2 = 40/2 = 20 cm

Substituting the values into the mirror formula, we have:
1/20 = 1/v - 1/-30

To simplify the equation, we take the reciprocal of both sides:
20/1 = v/-30 - 1

Now, simplify further:
20 = -v/30 - 1

Multiply through by 30 to remove the denominators:
600 = -v - 30

Rearrange the equation to solve for v:
-v = 600 + 30
-v = 630

Multiply both sides by -1 to isolate v:
v = -630

Since v is negative, it indicates that the image is formed on the same side as the object. The image distance (-630 cm) tells us that the image is located 630 cm in front of the mirror.

Therefore, the location of the image is 630 cm in front of the concave mirror.

60cm