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A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 12.5 cm in such a way that they have the same p

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A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 12.5 cm in such a way that they have the same p

Question

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 12.5 cm in such a way that they have the same principal axis. Find the power of the combination

## Answers ( )

Answer:Focallengthofconcavelens–Powercalculatedas–PowerofconvexlensCalculatedas–Powerofcombination–FocallengthofconcavelensCalculatedas–Power–Focallengthofconvexlens–Powerofcombination–Answer:

Focal length of concave lens –

12.5 cm = – 0.125 m

Power calculated as –

\begin{gathered} \\ \sf \: p = \dfrac{1}{ – 0.125} \\ \\ \\ \qquad \bullet \sf \: – 8.3 \: D \\ \\ \end{gathered}

p=

−0.125

1

∙−8.3D

Power of convex lens Calculated as –

\begin{gathered} \\ \sf \: p = \dfrac{1}{0 – 20} \\ \\ \\ \qquad \bullet \sf \: – 5 \: D \\ \\ \end{gathered}

p=

0−20

1

∙−5D

Power of combination –

\begin{gathered} \\ \sf \: 5 – 8.3 \\ \\ \\ \implies \sf \: 3.3 \: D \\ \\ \end{gathered}

5−8.3

⟹3.3D

Focal length of concave lens Calculated as –

\begin{gathered} \\ \sf \: f = – 10 \: cm = \frac{ – 10}{100} \\ \\ \\ \qquad \bullet \sf \: 0.1 \: m. \\ \\ \end{gathered}

f=−10cm=

100

−10

∙0.1m.

Power –

\begin{gathered} \\ \sf \: p = \frac{1}{ – 0.1} \\ \\ \\ \qquad \sf \bullet \: 10 \: D \\ \\ \end{gathered}

p=

−0.1

1

∙10D

Focal length of convex lens –

20 cm = 0.2 m.

\begin{gathered} \\ \sf p = \dfrac{1}{f} \\ \\ \\ \sf \: p = \dfrac{1}{0.20} \\ \\ \\ \implies \sf \: 5 \: D \\ \\ \end{gathered}

p=

f

1

p=

0.20

1

⟹5D

Power of combination –

\begin{gathered} \\ \sf \: 5 – 10 \\ \\ \\ \implies \sf \blue{ – 5 \: D} \\ \\ \end{gathered}

5−10

⟹−5D