Plane Mirror

Image formed is as far behind the mirror as the object is in front of it, with the lateral inversion of image. i.e. right hand side of object is left hand side of image and vice versa.

Convex Mirror

Image formed is always virtual, erect and diminished.

Concave Mirror

Depending upon the position of the object, size of the image formed can be equal to, larger than or smaller than the size of object. Also the nature of image formed may be real or virtual.

Plane Mirror

Image formed is as far behind the mirror as the object is in front of it, with the lateral inversion of image. i.e. right hand side of object is left hand side of image and vice versa.

Convex Mirror

Image formed is always virtual, erect and diminished.

Concave Mirror

Depending upon the position of the object, size of the image formed can be equal to, larger than or smaller than the size of object. Also the nature of image formed may be real or virtual.

The distance between the principal focus of a mirror and the pole of mirror is called focal length of the mirror.

In case of Concave mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as negative.

In case of Convex mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as positive.

The radius of Curvature of plane mirror is infinite, hence the focal length of plane mirror will also be infinite.

The distance between the principal focus of a mirror and the pole of mirror is called focal length of the mirror.

In case of Concave mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as negative.

In case of Convex mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as positive.

The radius of Curvature of plane mirror is infinite, hence the focal length of plane mirror will also be infinite.

Solution: For a concave mirror u becomes negative, $$\therefore u = -7.5 cm $$ (i) When real image is formed v is also negative $$ \therefore v = -30 cm $$

By using mirror formula, $$ \frac { 1 }{ u } +\frac { 1 }{ v } =\frac { 1 }{ f } $$ Lets substitute the values, $$ \frac { 1 }{ -7.5 } +\frac { 1 }{ -30 } =\frac { 1 }{ f } $$ $$ \therefore \frac { 1 }{ f } = \frac { -30-7.5 }{ \left( -7.5 \right) \times \left( -30 \right) } = \frac { -37.5 }{ 225 } $$ $$ \therefore f = \frac { 225 }{ -37.5 } = -6 cm $$ (ii) When virtual image is formed v is positive $$ \therefore v = 30 cm $$ By using mirror formula, $$ \frac { 1 }{ u } +\frac { 1 }{ v } =\frac { 1 }{ f } $$ Lets substitute the values, $$ \frac { 1 }{ -7.5 } +\frac { 1 }{ 30 } =\frac { 1 }{ f } $$ $$ \therefore \frac { 1 }{ f } = \frac { 30-7.5 }{ \left( -7.5 \right) \times \left( 30 \right) } $$ $$= \frac { 22.5 }{ -225 } $$ $$ \therefore f = \frac { -225 }{ 22.5 } = -10 cm $$ Hence the focal length of mirror when real image is formed is -6 cm and when virtual image is formed at 30 cm, focal length of mirror will be -10 cm.

Solution: For a concave mirror u becomes negative, $$\therefore u = -7.5 cm $$ (i) When real image is formed v is also negative $$ \therefore v = -30 cm $$

By using mirror formula, $$ \frac { 1 }{ u } +\frac { 1 }{ v } =\frac { 1 }{ f } $$ Lets substitute the values, $$ \frac { 1 }{ -7.5 } +\frac { 1 }{ -30 } =\frac { 1 }{ f } $$ $$ \therefore \frac { 1 }{ f } = \frac { -30-7.5 }{ \left( -7.5 \right) \times \left( -30 \right) } = \frac { -37.5 }{ 225 } $$ $$ \therefore f = \frac { 225 }{ -37.5 } = -6 cm $$ (ii) When virtual image is formed v is positive $$ \therefore v = 30 cm $$ By using mirror formula, $$ \frac { 1 }{ u } +\frac { 1 }{ v } =\frac { 1 }{ f } $$ Lets substitute the values, $$ \frac { 1 }{ -7.5 } +\frac { 1 }{ 30 } =\frac { 1 }{ f } $$ $$ \therefore \frac { 1 }{ f } = \frac { 30-7.5 }{ \left( -7.5 \right) \times \left( 30 \right) } $$ $$= \frac { 22.5 }{ -225 } $$ $$ \therefore f = \frac { -225 }{ 22.5 } = -10 cm $$ Hence the focal length of mirror when real image is formed is -6 cm and when virtual image is formed at 30 cm, focal length of mirror will be -10 cm.

Solution: As we have a concave mirror focal length is negative, $$ \therefore f = -50 cm $$ and $$ Magnification (m) = \frac { v }{ u } = 2 $$ $$ \therefore v = 2u $$ By using mirror formula, $$ \frac { 1 }{ u } +\frac { 1 }{ v } =\frac { 1 }{ f } $$ Lets substitute the values, $$ \frac { 1 }{ u } +\frac { 1 }{ 2u } =\frac { 1 }{ -50 } \frac { 2+1 }{ 2u } $$ $$=\frac { -1 }{ 50 } \frac { 3 }{ 2u } $$ $$ =\frac { -1 }{ 50 } $$ $$ \therefore 2u = -\left( 3 \times 50 \right) $$ or $$ u = \frac { -150 }{ 2 } = -75 cm $$

Solution: As we have a concave mirror focal length is negative, $$ \therefore f = -50 cm $$ and $$ Magnification (m) = \frac { v }{ u } = 2 $$ $$ \therefore v = 2u $$ By using mirror formula, $$ \frac { 1 }{ u } +\frac { 1 }{ v } =\frac { 1 }{ f } $$ Lets substitute the values, $$ \frac { 1 }{ u } +\frac { 1 }{ 2u } =\frac { 1 }{ -50 } \frac { 2+1 }{ 2u } $$ $$=\frac { -1 }{ 50 } \frac { 3 }{ 2u } $$ $$ =\frac { -1 }{ 50 } $$ $$ \therefore 2u = -\left( 3 \times 50 \right) $$ or $$ u = \frac { -150 }{ 2 } = -75 cm $$

(i) The pole of mirror is taken as origin.

(ii) All distances are measured from the pole ‘O’ of the mirror.

(iii) Rays of light are assumed to be coming from left side and enter the right side.

(iv) Distances measured in the direction of incident ray are taken as positive.

(v) All distances measured in direction opposite to incident ray are taken as negative.

(vi) Height measured above the principal axis are taken as positive and below as negative.

(vii) For concave mirrors, radius of curvature (R) and focal length (f) are taken as negative.

(viii) For convex mirrors, radius of curvature (R) and focal length (f) are taken as positive.

(ix) For real image magnification is negative and for virtual image magnification is positive.

(i) The pole of mirror is taken as origin.

(ii) All distances are measured from the pole ‘O’ of the mirror.

(iii) Rays of light are assumed to be coming from left side and enter the right side.

(iv) Distances measured in the direction of incident ray are taken as positive.

(v) All distances measured in direction opposite to incident ray are taken as negative.

(vi) Height measured above the principal axis are taken as positive and below as negative.

(vii) For concave mirrors, radius of curvature (R) and focal length (f) are taken as negative.

(viii) For convex mirrors, radius of curvature (R) and focal length (f) are taken as positive.

(ix) For real image magnification is negative and for virtual image magnification is positive.