A spherical mirror produces an image of magnification -1 on a screen placed at a distance of 50 cm from the mirror.
(a) Write the type of mirror.
(b) Find the distance of the image from the object.
(c) Draw the ray diagram to show the image formation in this case.

Explanation

If magnification, `m =-1`
`v=50`cm
If the magnification has minus sign, then the image is real and inverted,
`therefore v=-50`(for real image)
`therefore m=(-v)/(u) " " rArr cancel(-)=(cancel(-)(-50))/(cancel(-)u) " " rArr u =-50`cm
(a) Since image is formed on the secreen therefore the mirror formed real image which is formed by concave mirror only.
(b) Image distance = 50 cm in front of the mirror.
(c) `(1)/(f)=(1)/(v)+(1)/(u)" "rArr " "(1)/(f)=(1)/(-50)+(1)/(-50)`
`(1)/(f)=-(1)/(50)-(1)/(50)" " rArr (cancel(-2))/(cancel(l50))=(-1)/(25)`
`therefore f =-25` cm
(d) Ray diagram: