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A 10mm long awl pin is placed vertically in front of a concave mirror. A 5mm long image of the awl pin is formed at 30cm in front of the mirror. What is the focal length of this mirror? Please solve the problem in sequence.
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A 10mm long awl pin is placed vertically in front of a concave mirror....
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A 10mm long awl pin is placed vertically in front of a concave mirror....
Solution:


Given:


  • Length of the awl pin, h = 10 mm

  • Image distance, v = -30 cm

  • Height of the image, hi = 5 mm



Formula Used:

The magnification of the mirror is given as:

m = -v/u = hi/h

Where,

m = Magnification

v = Image distance

u = Object distance

hi = Height of the image

h = Height of the object


The focal length of the mirror is given as:

1/f = 1/v + 1/u

Where,

f = Focal length of the mirror


Calculation:

As per the given data, the magnification of the mirror is given as:

m = hi/h = 5/10 = 0.5


Using the magnification formula, we can write:

m = -v/u

0.5 = -30/u

u = -60 cm


Now, using the formula for focal length, we have:

1/f = 1/v + 1/u

1/f = 1/-30 + 1/-60

1/f = -1/60

f = -60 cm


Answer:

Therefore, the focal length of the mirror is -60 cm.
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A 10mm long awl pin is placed vertically in front of a concave mirror. A 5mm long image of the awl pin is formed at 30cm in front of the mirror. What is the focal length of this mirror? Please solve the problem in sequence.
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