Question

A convex lens of power 4D and a concave lens of power2D are placed in contact with each other. An object of size 4cm is placed at a distance of 60cm in front of the lens. Find the position, nature and size of the image formed.

Answer 1

Answer:

So position of image = 300 cm

Nature = Real and Inverted

Hence, the height of image = - 20 cm

Explanation:

Given,

Power of Convex Lens, P1 = + 4 D

Power of Concave Lens, P2 = - 2 D

Position of object, u = - 60 cm

Height of object, h = 4 cm

Power of combination, P = P1 + P2

=> P = +4 - 2 = 2 D

Let the focal length of the combination of lens be 'f'.

We know that,

Power = 1 / focal length (in meters)

=> P = 1 / f

=> f = 1 / P

=> f = 1/2 = 0.5 m = 50 cm

Hence, focal length of the combined lens = + 50 cm

Let the position of image be 'v'.

By lens formula, we know that,

1 / f = 1 / v + 1 / u

=> 1 / v = 1 / f + 1 / u

=> 1 / v = 1 / 50 + (- 1) / 60

=> 1 / v = (6 - 5) / 300 = 1 / 300

=> v = 300/1 = 300 cm

So position of image = 300 cm

Since, the position of image is positive. Hence, the image is formed on the opposite side of the lens. So the image is real and inverted and the lens is Convex Lens.

Nature = Real and Inverted

Let the height of image be h'. Then,

We know that,

Magnification, m = h' / h = v / u

=> h' / h = v / u

=> h' / 4 = 300 / (-60)

=> h' = 4 × (-5)

=> h' = -20 cm

Hence, the height of image = - 20 cm

(as image is real and inverted)

Answer 2

Answer :

Given -

• Power of convex lens is 4D.
• Power of concave lens is - 2D.
• The lenses are placed in contact.
• Object size = 4 cm.
• Object Distance = 60 cm.

To Find -

• Position of Image ?
• Nature of Image ?
• Size of Image ?

Solution -

Power = Power 1 + Power 2.

Power = 4 - 2 = 2 D.

Focal length = 1/Power = 1/2 = 0.5 m = 50 cm.

Lens Formula : 1/f = 1/v - 1/u.

⇒ 1/50 = 1/v - 1/-60

⇒ 1/v = 1/50 - 1/60

⇒ 1/v = (60 - 50)/3000

⇒ 1/v = 10/3000

⇒ 1/v = 1/300

⇒ v = 300 cm

Hence, Image Distance = 300 cm.

The position of the Image : Beyond 2F2.

The size of the Image : Enlarged.

The Nature of the Image : Real and Inverted.

Now, Magnification = h'/h = v/u.

⇒ h' = 300/-60*4

⇒ h' = 30/-6*4

⇒ h' = -5*4

⇒ h' = -20 cm

Hence, Height of the Image = -20 cm.