Question

An object of height 5 cm is placed 20cm in front of a concave mirror of focal length 15 cm find the image distance and calculate the size of the image formed

Answer 1

Given :

Object height = 5cm

Object distance = -20cm

Focal length = -15cm

Mirror : concave mirror

Note : In concave mirror focal length is always negative.

To find :

The image distance a nd the size of the image formed.

Solution :

using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

$\boxed{ \bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

now, substituting all the given values,

$\leadsto{ \sf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

$\leadsto{ \sf \dfrac{1}{v} + \dfrac{1}{( - 20)} = \dfrac{1}{( - 15)} }$

$\leadsto{ \sf \dfrac{1}{v} - \dfrac{1}{20} = - \dfrac{1}{15} }$

$\leadsto{ \sf \dfrac{1}{v} = - \dfrac{1}{15} + \dfrac{1}{20} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{ - 4 + 3}{60} }$

$\leadsto{ \sf \dfrac{1}{v} = - \dfrac{ 1}{60} }$

$\leadsto{ \sf v = - 60 \: cm }$

thus, the image distance is -60cm.

» The Magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign and is also equal to the ratio of height of the image to the height of the object .i.e.,

$\boxed{ \bf m = - \dfrac{v}{u} = \dfrac{h'}{h}}$

where,

• v denotes image distance
• u denotes object distance
• h' denotes image height
• h denotes object height

Now, substituting all the given values in the formula,

$\leadsto{ \sf -\dfrac{v}{u} = \dfrac{h'}{h} }$

$\leadsto{ \sf -\dfrac{( - 60)}{( - 20)} = \dfrac{h'}{5} }$

$\leadsto{ \sf -3 = \dfrac{h'}{5} }$

$\leadsto{ \sf h' = - 3 \times 5 }$

$\leadsto{ \sf h' = - 15 \: cm}$

thus, the size of the image is -15cm.

The minus signhere shows that the image is formed below the principle axis. This is the image is real and inverted.