A convex lens has a focal length of 15 cm. At what distance should an object be placed in front of the lens to get a real image of the same size of the object ?

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Q: 23 (CDS-I/2022)
A convex lens has a focal length of 15 cm. At what distance should an object be placed in front of the lens to get a real image of the same size of the object ?

question_subject: 

Maths

question_exam: 

CDS-I

stats: 

0,77,54,33,19,77,2

keywords: 

{'focal length': [1, 0, 5, 7], 'convex lens': [0, 0, 0, 4], 'lens': [0, 0, 0, 1], 'distance': [0, 3, 3, 3], 'real image': [0, 0, 0, 1], 'object': [1, 0, 11, 43], 'cm': [2, 0, 7, 20], 'front': [1, 0, 4, 7]}

To determine the distance at which an object should be placed in front of a convex lens to get a real image of the same size, we can use the lens formula:

1/f = 1/v - 1/u

Where:

- f is the focal length of the lens

- v is the distance of the image from the lens

- u is the distance of the object from the lens

In this case, the focal length of the lens is given as 15 cm (f = 15 cm). Since we want to obtain a real image of the same size as the object, the magnification of the image should be 1.

Therefore, the magnification formula can be used:

magnification = -v/u

Since the magnification is 1, we can rewrite the formula as:

1 = -v/u

By substituting the given focal length (f = 15 cm) and simplifying the equation, we get:

-15/u = 1

Solving for u, we find:

u = -15 cm

Now, since u represents the distance of the object from the lens, it must be positive. Therefore, the distance at which the object should be placed in front of the lens to get a real image of the