1.an object is placed in front of concave mirror of focal length 20 Cm, the image formed is 3 times the size of the object.find the image distance.
2.A 2.5 cm candle is placed 12 cm away from a convex mirror of focal length 30 cm.find the location of the image and magnification of the image.
dkavyasri13:
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Answered by
2
1. f = -20cm
m = -3
v = ?
m = -v/u = -3
⇒ v/u = 3
⇒ v = 3u
Using mirror formula 1/v + 1/u = 1/f
⇒ 1/3u + 1/u = 1/-20
⇒ (1+3)/3u = 1/-20
⇒ 4/3u = 1/-20
⇒ u = -(4*20)/3
⇒ u = -80/3 cm
v = 3u = -80/3 * 3 = -80cm
∴ Image distance from mirror is 80cm. It is formed in front of the mirror.
2. h = +2.5cm
u = -12cm
f = +30cm
v = ?
m = ?
1/v + 1/u = 1/f
⇒ 1/v = 1/f - 1/u = 1/30 - 1/-12
⇒ 1/v = 1/30 + 1/12
⇒ 1/v = (2+5)/60 = 7/60
⇒ v = 60/7 cm
m = -v/u = -(60/7)/(-12) = 60/(7*12) = 5/7
∴ Object distance is 60/7 from mirror. Image is virtual and erect(since v is positive). Magnification is 5/7.
m = -3
v = ?
m = -v/u = -3
⇒ v/u = 3
⇒ v = 3u
Using mirror formula 1/v + 1/u = 1/f
⇒ 1/3u + 1/u = 1/-20
⇒ (1+3)/3u = 1/-20
⇒ 4/3u = 1/-20
⇒ u = -(4*20)/3
⇒ u = -80/3 cm
v = 3u = -80/3 * 3 = -80cm
∴ Image distance from mirror is 80cm. It is formed in front of the mirror.
2. h = +2.5cm
u = -12cm
f = +30cm
v = ?
m = ?
1/v + 1/u = 1/f
⇒ 1/v = 1/f - 1/u = 1/30 - 1/-12
⇒ 1/v = 1/30 + 1/12
⇒ 1/v = (2+5)/60 = 7/60
⇒ v = 60/7 cm
m = -v/u = -(60/7)/(-12) = 60/(7*12) = 5/7
∴ Object distance is 60/7 from mirror. Image is virtual and erect(since v is positive). Magnification is 5/7.
Answered by
3
1)
f = -20 cm m = 3 or - 3 either of them.
case1) m = -v/u = -3 => v = 3 u inverted image
1/f = 1/v + 1/u => 1/-20 = 1/v + 3/v = 4/v
=> v = - 80 cm
case 2) m = -v/u = 3 => erect virtual image. v = - 3 u
1/-20 = 1/v - 3/v = - 2/v
=> v = 40 cm
============================
2)
u = -12 cm h = 2.5 cm
f = +30 cm
1/f = 1/v + 1/u
1/30 = 1/v -1/12 => v = 60/7 cm virtual image, behind the mirror.
m = -v/u = 5/7
f = -20 cm m = 3 or - 3 either of them.
case1) m = -v/u = -3 => v = 3 u inverted image
1/f = 1/v + 1/u => 1/-20 = 1/v + 3/v = 4/v
=> v = - 80 cm
case 2) m = -v/u = 3 => erect virtual image. v = - 3 u
1/-20 = 1/v - 3/v = - 2/v
=> v = 40 cm
============================
2)
u = -12 cm h = 2.5 cm
f = +30 cm
1/f = 1/v + 1/u
1/30 = 1/v -1/12 => v = 60/7 cm virtual image, behind the mirror.
m = -v/u = 5/7
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