Question

a lighted candle is placed at a distance of 40cm from vertical wall. where a concave mirror of radius of curvature 30cm should be placed so that an image of the flame is obtained on the wall?
it's urgent​

Answer 1

Answer:

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

Now, as per as the Question, Image Height = 4 x 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,

1 f 1 ย 1 1 f 1 -160 + 1 -40

On Multiplying both sides by 160,

We get,

160 f

160 160 -160 + -40

⇒ 160/f = -1-4

⇒ 160/f = -5 ⇒ f = 160/-5

⇒ f = -32 cm.

• Focal length of the Concave Mirror is

32 cm.

100%

Now, For the Radius of the Curvature,

Using the Formula,

Focal Length = Radius Of Curvature/2 .. Radius of Curvature = Focal Length x

2

.. R = F x2

R = 32 x 2

.. R = 64 cm.

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