The nature of image of a candle flame located 40cm from a concave spherical mirror is real, inverted and magnified four times. Then the radius of curvature of the mirror is:
The nature of image of a candle flame located 40cm from a concave spherical mirror is real, inverted and magnified four times. Then the radius of curvature of the mirror is:
The correct option is A 64 cm
Distance of the Candle from the Concave Mirror
(u) = 40cm.(negative)
Now, as per as the Question,
ImageHeight=4×Object(orCandle)Height
ImageHeight/CandleHeight=4
Magnification = 4
[ Magnification = Image Height/Object Height]
Now, Magnification = −v/u
4=−v/u
−v=4u
v=−4u
v=−4×40
v=−160cm.
Now, Image Distance(v) = - 160cm.
Using the Mirror's Formula,
On Multiplying both sides by 160 ,
We get,
⇒ 160/f=−1−4
⇒ 160/f=−5
⇒ f=160/−5
⇒ f=−32cm.
∴ Focal length of the Concave
Mirror is 32 cm.
Now, For the Radius of the Curvature,
Using the Formula,
FocalLength=RadiusOfCurvature/2
∴ RadiusofCurvature=FocalLength×2
∴ R=F×2
∴ R=32×2
∴ R=64cm.
Hence, the Radius of the Curvature of the Concave
mirror of Focal Length 3 cm is 64 cm.
Distance of the Candle from the Concave Mirror (u) = 40cm.(negative)
Now, as per as the Question,
ImageHeight=4×Object(orCandle)Height
ImageHeight/CandleHeight=4
Magnification = 4
[ Magnification = Image Height/Object Height]
Now, Magnification = −v/u
4=−v/u
−v=4u
v=−4u
v=−4×40
v=−160cm.
Now, Image Distance(v) = - 160cm.
Using the Mirror's Formula,
On Multiplying both sides by 160 ,
We get,
⇒ 160/f=−1−4
⇒ 160/f=−5
⇒ f=160/−5
⇒ f=−32cm.
∴ Focal length of the Concave Mirror is 32 cm.
Now, For the Radius of the Curvature,
Using the Formula,
FocalLength=RadiusOfCurvature/2
∴ RadiusofCurvature=FocalLength×2
∴ R=F×2
∴ R=32×2
∴ R=64cm.
Hence, the Radius of the Curvature of the Concave mirror of Focal Length 3 cm is 64 cm.
