Question

Question:
An inverted image is magnified by 2 when an object is placed 22 cm in front of a concave mirror. Determine the image distance and focal length of the mirror

Answer 1

Answer:

v = - 44 cm ,f = - 14.6 cm

Explanation:

m= -2

u= - 22

m=v/u

-2=V/22

-2 ×22 = V

v=-44 cm

now we know the value of v , by using mirror formula we can find out focal length (f)

1/f=1/v+1/u

= 1/45 + 1/-22

= -14.6 cm

Answer 2

The image distance and focal length of the mirror are 44cm and 14.66cm.

Given:

The inverted image is magnified by 2.

An object is placed 22cm in front of a concave mirror.

To Find:

The image distance and focal length of the mirror.

Solution:

Here, it is given that the object is placed $22cm$ in front of a concave mirror.

so, $\frac{1}{f} =\frac{1}{d_o}+\frac{1}{d_i}$

where, $do=22cm$

and,

$M=2$.

Now, firstly find the image distance by using the magnification equation.

here we get,

$M=-\frac{d_i}{d_o}$

here, after putting the given values in the above equation.

we get,

$d_i=-Md_o$

$=-(-2).22cm\\=44cm.$

now, calculate the focal length of the mirror by using the mirror equation.

$\frac{1}{d_o} +\frac{1}{d_i}=\frac{1}{f}$

here,

$f=\frac{1}{\frac{1}{d_o}+\frac{1}{d_i} } \\f=\frac{1}{\frac{1}{22cm}+\frac{1}{44cm} } \\f=14.66cm.$

Hence, the image distance and focal length of the mirror are 44cm and 14.66cm.

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