Rajashree wants to get an inverted image of height 5 cm of an object kept at a distance of 30 cm from a concave mirror. The focal length of the mirror is 10 cm. At what distance from the mirror should she place the screen ? What will be the type of the image, and what is the height of the object?

Explanation

Focal length = f= - 10 cm , object distance = u =- 30 cm,
height of the image =` h_2 = - 5 cm `
Image distance = v= ? Height of object =`h_1 =? `
According to the mirror formula
` (1)/(v) +(1)/(u) = (1)/(f)`
` (1)/(v) = (1)/(f) - (1)/(u)`
` (1)/(v) = (1 )/(-10) - (1)/(-30 ) `
` (1)/(v) = (-3 +1)/(30 ) `
` (1)/(v) = (-2)/(30)`
` (1)/(v) = (1)/(-15) ` cm
` v= - 15`
Magnification
` M= (h_2)/(h_1) = - (v)/(u)`
` h_1= - (uh_2)/(v) `
`h_1 = - ((-30)(-5))/(-15)`
` h_1= (-2) (-5)`
`h_1 = 10 cm `
The height of the object is 10 cm. Thus, the image will be real and diminshed.
Rajashree has to place the screen 15 cm to the left of the mirror.