Question

If the power of combination is 4D power of lens 1 is -2.5D then find the power of lens 2 and also find out focal length of the combination.​

Answer 1

Answer:

To find the power of the combination of two lenses, we use the formula:

⇒ P = P₁ + P₂

According to the question,

P = 4 D

P₁ = -2.5 D

P₂ = ?

Substituting the information we get:

⇒ 4 D = -2.5 D + P₂

⇒ P₂ = 4 D - ( -2.5 D ) = 4 D + 2.5 D

⇒ P₂ = 6.5 D

Hence the power of the second lens is 6.5 D.

We know that, Power is defined as the reciprocal of Focal length in meters. Therefore we get:

⇒ P = 1 / f

⇒ 4 = 1 / f

⇒ f = 1 / 4

⇒ f = 0.25 m (or) 25 cm

Hence the focal length of the combination of two lenses is 25 cm (or) 0.25 m.

Answer 2

$\large\underline{\underline{\text{Question:}}}$

• If the power of combination is 4D power of lens 1 is -2.5D then find the power of lens 2 and also find out focal length of the combination.

$\large\underline{\underline{\text{Solution:}}}$

As given,

• $\text{The power of combination of 2 lens }(P_{(\text{Combination lens})}) = 4D$
• $\text{The power of lens 1 }(P_1) = - 2.5D$

As we know that,

$\longrightarrow \boxed{P_{(\text{Combination lens})} = P_{1} + P_{2}}$

Let us substitute the given values,

$\longrightarrow 4D = - 2.5D + P_{2}$

$\longrightarrow P_{2} = 4D + 2.5D$

We get,

$\longrightarrow \boxed{ P_{2} = 6.5D }$

Therefore,

• $\text{The power of lens 2 }(P_2) = 6.5D$

As we know that,

$\longrightarrow \boxed{P = \frac{1}{f} }$

So we can say that,

$\longrightarrow P_{(\text{Combination lens})} = \frac{1}{f_{(\text{Combination lens})}}$

$\longrightarrow 4D = \frac{1}{f_{(\text{Combination lens})}}$

$\longrightarrow 4D \times f_{(\text{Combination lens})} = 1$

$\longrightarrow f_{(\text{Combination lens})} = \frac{1}{4D }$

$\longrightarrow f_{(\text{Combination lens})} = \frac{1}{4 } \times \frac{1}{D}$

$\longrightarrow f_{(\text{Combination lens})} = \frac{1}{4 }m \: \: \: \: \: \: \: \: ... [ \frac{1}{D} = 1m]$

$\longrightarrow \boxed{f_{(\text{Combination lens})} = 0.25m}$

Therefore,

• $\text{The focal length of combination of lens is 0.25m}$

$\large\underline{\underline{\text{Required Answer:}}}$

• The power of lens 2 is 6.5D.

• The focal length of combination of lens is 0.25m.