An object of 4.0 cm in size is placed at 25 cm in front of a concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image?

Question

Which of the following statements are correct?
(A) All mirrors follow the laws of reflection.
(B) The angle between the ray of incidence and the plane surface of the mirror is equal to the angle between the plane surface of mirror and the ray of reflection for plane mirror
(C) the rays coming parallel to the principal axis will go after reflection through the focus of the curved mirror
(D) the rays coming to the pole of a curved mirror making an angle with axis will be reflected making the equal angle with the axis on the other side of the axis.
Choose the correct answer from the options given below:

Answer 1

To find the image distance \( v \), we use the mirror equation:\n\[\n\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\n\]\nWhere:\n- \( f = 15 \, \text{cm} \)\n- \( u = -25 \, \text{cm} \)\n\nSubstituting:\n\[\n\frac{1}{15} = \frac{1}{-25} + \frac{1}{v}\n\]\nSolving for \( v \):\n\[\n\frac{1}{v} = \frac{1}{15} + \frac{1}{25} = \frac{5 + 3}{75} = \frac{8}{75}\n\]\n\[\nv = \frac{75}{8} = 9.375 \, \text{cm}\n\]\n\nTherefore, the image forms at \( 9.375 \, \text{cm} \).

An object of 4.0 cm in size is placed at 25 cm in front of a concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image?

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The Correct Option is C

Solution and Explanation

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