Question

An object placed at a distance of 10 cm from the pole of a concave mirror. its image is formed at 6 cm from its pole on the same side of the object. calculate focal length

Answer 1

Answer :

Given -

• Object Distance = - 10 cm
• Concave mirror
• Image is formed at the same side of the object
• Image Distance = - 6 cm

To Find -

• Focal length ?

Solution -

Mirror Equation : 1/f = 1/v + 1/u

⇒ 1/f = 1/-6 + 1/-10

⇒ 1/f = -1/6 - 1/10

⇒ 1/f = (-10 - 6)/60

⇒ 1/f = -16/60

⇒ 60 = -16f

⇒ f = 60/-16

⇒ f = - 3.75 cm

So, the focal length of the concave mirror is (- 3.75) cm.

Answer 2

Given :

• Object Distance (u) = - 10 cm
• Image Distance (v) = - 6 cm
• Concave mirror

To Find :

• Focal length of the mirror

Solution :

We're given that the object distance is - 10 cm and image distance is - 6 cm. so, we can calculate value of Focal length using mirror formula :

$\bigstar \: \boxed{\sf{\dfrac{1}{f} \: = \: \dfrac{1}{v} \: + \: \dfrac{1}{u}}}$

Where,

• u is object distance
• v is image distance
• f is focal length

⇒1/f = 1/v + 1/u

⇒1/f = -1/6 + (-1/10)

⇒1/f = (-1/6) - (1/10)

⇒1/f = -[(5 + 3)/30]

⇒1/f = -8/30

⇒f = -30/8

⇒f = - 3.75

$\therefore$ Focal length of concave mirror is - 3.75 cm