An object of 2 cm height is placed at a distance of 30 cm in front of a concave mirror with radius of curvature 40 cm. The height of the image is ________ cm.Correct answer is '4'. Can you explain this answer?

Question

Answer

Given data:
- Object height (h) = 2 cm
- Object distance (u) = -30 cm (negative sign indicates that the object is placed in front of the mirror)
- Radius of curvature (R) = -40 cm (negative sign indicates concave mirror)

Formula:
The magnification (m) of an image formed by a mirror is given by the formula:
m = -v/u

Where,
- v = image distance
- u = object distance

Step 1: Calculating the image distance (v)
Using the mirror formula:
1/f = 1/v - 1/u

Substituting the given values:
1/(-40) = 1/v - 1/(-30)

Simplifying the equation:
-3/1200 = 1/v + 1/30

Solving for v:
1/v = -3/1200 - 1/30
1/v = (-3 - 40)/1200
1/v = -43/1200
v = -1200/43

Therefore, the image distance (v) is approximately -27.91 cm.

Step 2: Calculating the height of the image (h')
The height of the image (h') can be determined using the magnification formula:
m = -h'/h

Substituting the given values:
-27.91/-30 = -h'/2

Simplifying the equation:
0.9303 = -h'/2

Solving for h':
h' = -0.9303 * 2
h' = -1.8606

Since the height of an image cannot be negative, we take the absolute value:
h' = 1.8606 cm

Therefore, the height of the image is approximately 1.8606 cm, which can be rounded off to 2 cm.

The correct answer is 2 cm.

Note:
Since the question asks for the height of the image, the answer should be positive. It seems there might have been an error in the given correct answer, as the height of the image should not be 4 cm.

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