Question

What is the focus distance of a combined lens made by combining
a concave lens of 25 cm focus distance placed in contact with a
convex lens of 20 cm focus distance? Whether this combination is
convergent lens or Divergent​

Answer 1

Question:

What is the focus distance of a combined lens made by combining a concave lens of 25 cm focus distance placed in contact with a convex lens of 20 cm focus distance Whether this combination is convergent lens or Divergent

Given:

• Focal length of Concave lens be

(f¹) = - 25 cm

• Focal length of Convex lens be

(f²) = + 20 cm

To Find:

• Combination is convergent lens or Divergent

Formula Used:

• $\sf \: \dfrac { 1 } { f } = \dfrac { 1 } { { f }^{ 1 } } + \dfrac { 1 } { { f }^{ 2 } }$

• Power (P) = P¹ + P²

Solution:

Now Using,

• $\sf \: \dfrac { 1 } { f } = \dfrac { 1 } { { f }^{ 1 } } + \dfrac { 1 } { { f }^{ 2 } }$

We get,

Focal length of combination lens:

$\frac{1}{f} = \: \frac{1}{ {f}^{1} } + \frac{1}{ {f}^{2} } \\ \\ = \frac{1}{ - 25} + \frac{1}{20} \\ \\ \frac{1}{f} = - \frac{1}{100}$

We know that,

• f¹ = - 25 cm

• f² = + 20 cm

Now,

$\frac{1}{f} \div {f}^{1} = \frac{ - 25}{100} \\ \\ = - \: 0.25 \\ \\</p><h3> \frac{1}{f} \div {f}^{2} = \frac{20}{100} \\ \\ = 0.20$

Power: $\dfrac { 1 } { { p }^{ 1 } } + \dfrac { 1 } { { p }^{ 2 } }$

= $- \dfrac { 1 } { 0.25 } + \dfrac { 1 } { 0.20 }$

= $\dfrac { - 4 + 5 } { 1 }$

= $\dfrac { 5 - 4 } { 1 }$

Power = 1

The combination is convergent

$~~~$

Additional Info:

• If combination lens come with negative sign then power of lens be Divergent.

• If combined lens come with positive sign then power of lens be Convergent.

Hope it helps ya!!

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Answer 2

The combination is divergent.

The net focal length of the combination of lens can be found by using the following formula:

       $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}$

           $= \frac{1}{25} + \frac{1}{-20}$

           $= - \frac{1}{100}$

⇒ f = -100 cm

Thus the combined power,

          P = P₁ + P₂

              $= \frac{1}{f_1} + \frac{1}{f_2}$

             $= \frac{1}{0.25} + \frac{1}{-0.20}$

             $= \frac{100}{25} - \frac{100}{20}$

             $= -\frac{100}{100}$

             = -1

⇒ P = -1D

Here, the power is negative. Thus the combination is diverging.

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