A square ABCD of side 1 mm is kept at distance 15 cm in front of the concave mirror as shown in figure. The focal length of the mirror is 10 cm. The length of the perimeter of its image will be

The problem involves the use of the mirror formula and magnification formula in optics.

1. The mirror formula is 1/f = 1/v + 1/u. Here, f is the focal length of the mirror, v is the image distance, and u is the object distance.

2. The magnification formula is m = -v/u. Here, m is the magnification.

Given, u = -15 cm (the negative sign indicates that the object is on the same side as the light being reflected) and f = -10 cm (the negative sign indicates a concave mirror).

Step 1: Substitute the given values in the mirror formula to find v.

1/f = 1/v + 1/u 1/(-10) = 1/v + 1/(-15) Solving this equation gives v = -30 cm.

Step 2: Substitute the values of v and u in the magnification formula to find m.

m = -v/u = -(-30)/-15 = -2

The magnification is -2. The negative sign indicates that the image is inverted.

Step 3: The side of the square ABCD is 1 mm. The image formed by the mirror will have its side magnified by a factor of 2 (the absolute value of m), so the side of the image is 2 mm.

Step 4: The perimeter of a square is given by 4 times the side length. So, the perimeter of the image is 4 * 2 mm = 8 mm.

So, the length of the perimeter of the image of the square ABCD will be 8 mm.