At what distance should an object be placed from a convex mirror of focal length 40 cm so as to obtain an image th the size of the object?

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CONCEPT:

• A convex lens is a spherical surface Lens that helps in converging all the light at a single point. 
• An image formed is erect and virtual. Enlarged if the object is placed between lens and 2F and otherwise Diminished.
• The focal length of the Convex Lens is Positive.
• The relation between the distance of the image, object, and focal length is 

​\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\),

where f is focal length, v is the distance of the image, and u is the distance of the object.

• The magnification is given as,

\(\Rightarrow m=\frac{-v}{u}=\frac{h_{I}}{h_{o}}\)    

Where hI = height of the image and ho = height of the object

SOLUTION:

Given: f = 15 cm, v = -u

\(\frac{1}{15}=\frac{1}{-u}-\frac{1}{u} \Rightarrow \frac{1}{15}=\frac{-2}{u} \Rightarrow u=-30~cm\)

• Hence, the object should be placed at a distance of 30 cm from the lens.

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