How far must a girl stand in front of a concave spherical mirror of radius 120 cm to see an erect image of her face four times its natural size?

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Q: 67 (NDA-I/2009)
How far must a girl stand in front of a concave spherical mirror of radius 120 cm to see an erect image of her face four times its natural size?

question_subject: 

Maths

question_exam: 

NDA-I

stats: 

0,5,9,6,5,2,1

keywords: 

{'concave spherical mirror': [0, 0, 1, 0], 'radius': [0, 0, 2, 2], 'mirror': [0, 0, 0, 1], 'natural size': [0, 0, 1, 0], 'erect image': [0, 0, 1, 0], 'front': [1, 0, 4, 7], 'girl': [0, 1, 1, 1], 'cm': [2, 0, 7, 20], 'face': [0, 0, 7, 2]}

To find the correct answer, we need to understand the concept of magnification and the positioning of the object (girl`s face) in relation to the mirror.

In a concave spherical mirror, an object placed between the mirror`s focus and the mirror will produce an enlarged and erect image. The distance between the object and the mirror is called the object distance, and the distance between the image and the mirror is called the image distance.

The formula for magnification is given by m = -di/do, where m is the magnification, di is the image distance, and do is the object distance.

In this case, the magnification is given as four times the natural size, which means m = 4. Since the image is erect, the magnification should be positive.

From the formula, we can rearrange it to solve for di: di = -do/m.

Plugging in the values, we have di = -(-120 cm)/4 = 30 cm.

Since the image is formed on the same side as the object, the image distance is negative.

Therefore, the girl must stand 45 cm from the mirror (option 2) to see an erect image of her face four times its natural size.