Question

An object is placed at a distance of 20 cm from a concave mirror of a focal length 10cm. Find the position and magnification of image?? ​

Answer 1

Answer: Distance of image v = 20 cm

Explanation: object distance,u = -20cm

Focal length of convex lens f = 10cm

If the object is placed on the left side of the lens,then f=10cm;u=-20cm

1/f=1/u-1/v (image formula)

1/v=1/f+1/u

1/v=1/10+1/(-20)

1/v=20-10/200=10/200( zero zero cancel) =1/20

v=20cm

Distance of image v = 20cm

Inverted image at a distance of 20 cm on the right side of lens

m=v/u=20/-20= -1

(-ve sign indicates the inverted image).

[Nature of the image]

Answer 2

Answer:

Position of the image is in front of the concave mirror distance of 20 cm and image height and object height are equal.

Explanation:

Here given, object distance from the mirror is 20 cm and focal length is 10 cm.

According to the equation of spherical mirror,

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

Where u is object distance from the mirror and v is image distance from the mirror and f is focal length.

So,

$\frac{1}{v} + \frac{1}{ - 20} = - \frac{1}{10}$

$\frac{1}{v} = \frac{1}{20} - \frac{1}{10} = \frac{1 - 2}{20} = - \frac{1}{20}$

So,

$v = - 20 \: cm$

Therefore,the image will be formed in front of the concave mirror distance of 20 cm.

Now magnification of image

$= \frac{Size \: of \: the \: image}{Size \: of \: the \: object} = - \frac{v}{u} = - \frac{ - 20}{ - 20} = - 1$

This negative sign shows that the image is real.