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A $10 cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $12 cm$ . The distance from the object to the lens is $18 cm$ . Find the nature, position, and size of the image by choosing the correct option.

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Position:

33 cm

away from the lens, nature: Virtual and erect, size:

- 10 cm

Position:

36 cm

away from the lens, nature: Real and inverted, size:

- 20 cm

Position:

35 cm

away from the lens, nature: Real and inverted size:

20 cm

Position:

37 cm

away from the lens, nature: Real and inverted, size:

10 cm

answer is B.

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Detailed Solution

The position is

36 cm

away from the lens. And the image will be real and inverted.
The size of the image is

- 20 cm

and negative signs denote the nature of the image is inverted.
Given,
Object height,

h = + 10 cm

Focal length,

f = + 12 cm

Object distance,

u = - 18 cm

By Applying the Lens formula:

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

= > \frac{1}{v} = \frac{1}{f} + \frac{1}{u}

= > \frac{1}{v} = \frac{1}{12} + \frac{1}{- 18}

= > \frac{1}{v} = \frac{1}{12} - \frac{1}{18}

= > \frac{1}{v} = \frac{1}{36}

Substituting the respective values, we get;

v = + 36 cm .

Hence, the position of the image is 36 cm away from the lens and + sign denotes that the image is real. And the size of the image can be determined by

m = \frac{h'}{h} = \frac{v}{u}

\frac{h'}{10} = \frac{36}{- 18}

h ’ = - 20 cm

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A 10 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 12 cm. The distance from the object to the lens is 18 cm. Find the nature, position, and size of the image by choosing the correct option.

Detailed Solution

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A $10 cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $12 cm$ . The distance from the object to the lens is $18 cm$ . Find the nature, position, and size of the image by choosing the correct option.