Question

4.
An object is placed at a distance of 40 cm from
a concave mirror of focal length 15 cm. If the object
is displaced through a distance of 20 cm towards
temir Resisplacement of the image will be​

Answer 1

Given :

• Position of object, u = -40 cm
• Focal length of concave mirror, f = -15 cm

[ focal length of concave mirror is always negative ]

• New position of object when it is shifted 20 cm towards the mirror, u' = -40 + 20 = -20 cm

To find :

• Displacement in the position of image

Knowledge required :

• Mirror Formula

     1/f = 1/v + 1/u

[ where f is focal length, u si position of object and v is position of image ]

Solution :

Let, position of image when object is placed at 40 from the mirror be v

then, Using mirror formula

→ 1/f = 1/v + 1/u

→ 1/(-15) = 1/v + 1/(-40)

→ 1/(-15) + 1/40 = 1/v

→ 1/v = (-8 + 3) / (120)

→ 1/v = -5 / 120

→ v = 120 / -5

→ v = -24 cm

Now,

Let, position of image when object is shifted 20 cm towards the mirror such that position of object becomes -20 cm be v'

again, Using mirror formula

→ 1/f = 1/v' + 1/u'

→ 1/(-15) = 1/v' + 1/(-20)

→ 1/(-15) + 1/20 = 1/v'

→ 1/v' = (-4 + 3) / (60)

→ 1/v' = (-1) / 60

→ v' = - 60 cm

Therefore,

• On shifting object 20 cm towards the mirror then Image of object will be shifted ( 60 - 24 ) means 36 cm away from the mirror.