Question

The nature of image of a candle flame located 40 cm from a concave spherical mirror is real inverted and magnified 4 times then radius of curvature of mirror is

Answer 1

Hello Dear.

Here is the answer---

Distance of the Candle from the Concave Mirror (u) = 40 cm.(negative)

Now, as per as the Question,
 Image Height = 4 × Object (or Candle) Height
∴ Image Height/Candle Height = 4
∴ Magnification = 4
[ ∵ Magnification = Image Height/Object Height]

Now, Magnification = -v/u
∴ 4 = -v/u
∴ -v = 4u
⇒ v = -4u
⇒ v = -4 × 40
⇒ v = -160 cm.

Now, Image Distance(v) = - 160 cm.

Using the Mirror's Formula,

  $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
⇒ $\frac{1}{f} = \frac{1}{-160} + \frac{1}{-40}$
 
 On Multiplying both sides by 160 ,
We get,
$\frac{160}{f} = \frac{160}{-160} + \frac{160}{-40}$
⇒  160/f = -1 - 4
⇒ 160/f = -5
⇒ f = 160/-5
⇒ f = -32 cm.

∴ Focal length of the Concave Mirror is 32 cm.


Now, For the Radius of the Curvature,

Using the Formula,

  Focal Length = Radius Of Curvature/2
∴ Radius of Curvature = Focal Length × 2
∴ R = F × 2
∴ R = 32 × 2
∴ R = 64 cm.


Hence, the Radius of the Curvature of the Concave mirror of Focal Length 3 cm is 64 cm.


Hope it helps.

Answer 2

Answer: simplest method :-

Thank you

Step-by-step explanation: