Concave and convex lenses, each has the same focal length 20 cm and they are put in contact to form a combination lens. This combination lens is used to view an object of 5 cm length, kept at a distance 20 cm from the lens combination. As compared to the object, the image will be?

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Magnified and inverted

Reduced and erect

Of the same size as the object and erect

Of the same size as the object but inverted.

answer is C.

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Detailed Solution

Concept: When a concave and convex lens having the same focal lengths are in contact then the power becomes zero and focal length is finite. This combination acts as a glass plane.
As given,
Focal length of the convex lens is 20 cm
Focal length of the concave lens is -20 cm.
So, the effective focal length of this combination will be:

\frac{1}{f_{eff .}}

\frac{1}{f_{concave .}}

\frac{1}{f_{convex}}

\frac{1}{- 20}

\frac{1}{20}

= 0
Which proves that the focal length is finite.
Here, u is 20cm.
So, we also know that

\frac{1}{f_{eff .}}

\frac{1}{v}

–

\frac{1}{u}

⇨ 0 =

\frac{1}{v}

–

\frac{1}{20}

⇨

\frac{1}{v}

\frac{1}{20}

m
⇨ V = 20cm
Magnification is v/u = 1
Since the length of both the object and the image is the same.
Hence, , the image formed will be of the same size and erect.
Hence, the correct option is 3.

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