A concave shaving mirror is construction so that a man at a distance of 20 cm from the mirror sees his image magnified 1.5 times . what is the radius of curvature of the mirror ?
Answers
Given :
→ position of object (person) , u = -20 cm
→ Magnification produced by concave mirror , m = 1.5
( positive magnification because image is seen by the person and hence , the image will be virtual and erect )
To find :
→ Radius of curvature of mirror , R = ?
Formulae required :
Formula for magnification of mirror
- m = - v / u
Mirror formula
- 1/f = 1/v + 1/u
Radius of curvature is twice the focal length of mirror
- R = 2 f
( where m is magnification , f is focal length , R is radius of curvature , v is position of image and u is position of object )
Solution :
Let , position of image = v
focal length of mirror = f
Using formula for magnification
→ m = - v / u
→ 1.5 = - v / -20
→ - v = 1.5 × (-20)
→ - v = -30
→ v = 30 cm
Using Mirror formula
→ 1/f = 1/v + 1/u
→ 1/f = 1/(30) + 1/(-20)
→ 1/f = (2-3) / 60
→ 1/f = -1 / 60
→ f = -60 cm
Using formula R = 2 f
→ R = 2 f
→ R = 2 (-60)
→ R = -120 cm
therefore,
Radius of curvature of mirror is 120 cm . ( where negative sign in R = -120 cm shows that Center of curvature is on negative principal axis. )
Explanation:
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