Question

An object is kept at a distance of 100cm for lens of power -4D then the image distance is____​

Answer 1

Given :-

• An object is kept at a distance of 100cm for lens of power -4D.

To find :-

• Image distance

Solution :-

• Object distance (u) = 100cm

• Power (P) = - 4 D

As we know that

→ Power = It is the reciprocal of focal length

• According to question

→ P = 1/f

→ - 4 = 100/f

→ - 4f = 100

→ f = - 100/4

→ f = - 25 cm

According to lens formula

→ 1/v - 1/u = 1/f

→ 1/v = 1/u + 1/f

→ 1/v = -1/100 + (-1)/25

→ 1/v = - 1/100 - 1/25

→ 1/v = -1 - 4/100

→ 1/v = -5/100

→ 1/v = -1/20

→ v = - 20cm

Hence,

• Image distance is - 20cm

Answer 2

Given Parameters :

• Object Distance (u) = 100 cm
• Power (P) = -4 D

Answer:

As we know that,

• Power = ¹/f

Therefore,

→ -4 D = ¹/f

→ f = ¹/-4

→ f = -25 cm

❍ According to Question now,

➝ ¹/f = ¹/ᵥ - ¹/ᵤ

➝ ¹/ᵥ = ¹/ᵤ + ¹/f

➝ ¹/ᵥ = -1/100 - 1/25

➝ ¹/ᵥ = -1 - 4/100

➝ ¹/ᵥ = -5/100

➝ ¹/ᵥ = -1/20

➝ ¹/ᵥ = -20 cm

Therefore, the image Distance is -20 cm.