Question

an object is kept on the principle axis of a concave mirror of focal length 12cm.if the object of 18 cm from the mirror.
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Answer 1

CORRECT QUESTION:

An object is kept on the principal axis of a concave mirror of focal length 12 cm. If the object is at a distance of 18 cm from the mirror, calculate the image distance. Determine the nature of the image formed . Calculate the magnification produced by the mirror.

GIVEN:

• Focal length, f = - 12 cm
• Object distance, u = - 18 cm

TO FIND:

• Image distance, v
• Nature of image
• Magnification produced by mirror, m

FORMULAE:

• Mirror formula, 1/f = 1/v + 1/u

• Magnification of mirror, m = -v/u

SOLUTION:

STEP 1: TO FIND IMAGE DISTANCE:

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \\ \\ \frac{1}{ - 12} = \frac{1}{v} + \frac{1}{ - 18} \\ \\ - \frac{ 1}{12} = \frac{1}{v} - \frac{1}{18} \\ \\ - \frac{1}{12} + \frac{1}{18} = \frac{1}{v} \\ \\ \frac{1}{v} = \frac{ - 18 + 12}{12 \times 18} \\ \\ \frac{1}{v} = - \frac{6}{216} \\ \\ \frac{1}{v} = - \frac{1}{36} \\ \\ v = - 36 \: cm$

Image is at a distance of 36 cm to the left of principal point.

The image formed is real, since the rays actually meet.

STEP 2: TO FIND MAGNIFICATION:

$m = - \frac{v}{u} \\ \\ m = - (\frac{ - 36}{ - 18} ) \\ \\ m = - 2$

Magnification of mirror is -2.

Negative magnification indicates that the image is inverted.

ANSWERS:

• Image distance is - 36 cm

• The image is real and inverted.

• Magnification of concave mirror is -2.

POINTS TO REMEMBER:

• All points that lie to the left of principal point are taken negative.

• All points that lie to the right of principal point are taken positive.

• All points above the principal axis are positive .

• The points that lie below the principal axis are negative.

• Focal length of concave mirror is negative and convex mirror is positive.

• Magnification is positive for erect image and negative of inverted image in case of mirrors.

• For mirrors, if the object and the image are on same side, then the image is real. If they are on opposite side, the image is virtual.