A man uses a concave mirror for shaving he keeps his face at a distance of 25cm from the mirror and gets and image which is 1.4 times enlarged find the Focal length of the mirror ?

Question

Answer

Answer

Bhai use this formula m=F/F-U in this m=magnification and we have given 1.4 and U=Object distance and you find focal length but keep them with sign

Answer

Understanding the Problem
When a man shaves using a concave mirror, he positions his face 25 cm from the mirror. The image formed is 1.4 times enlarged, indicating that it is a virtual image.
Given Data
- Object distance (u) = -25 cm (negative as per the convention for concave mirrors)
- Magnification (m) = 1.4 (positive for virtual images)
Using the Magnification Formula
The magnification (m) for mirrors is given by the formula:
m = - (v / u)
Where:
- v is the image distance.
Since m = 1.4, we can rewrite the equation:
1.4 = - (v / -25)
This simplifies to:
v = 1.4 * 25 = 35 cm
Using the Mirror Formula
The mirror formula relates the object distance (u), image distance (v), and focal length (f):
1/f = 1/v + 1/u
Substituting the values:
1/f = 1/35 + 1/(-25)
This gives:
1/f = 1/35 - 1/25
Finding a common denominator (175):
1/f = (5 - 7) / 175 = -2 / 175
Thus,
f = -87.5 cm
Conclusion
The focal length of the concave mirror is approximately -87.5 cm. The negative sign indicates that the focal point is on the same side as the object, which is characteristic of concave mirrors. This setup allows the user to obtain a larger virtual image for easy shaving.

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