Question

A concave cosmetic mirror has a focal length of 40cm. A 5-cm-long mascara brush is held upright 20cm from the mirror. Use ray tracing to determine the location and height of its image. Is the image upright or inverted? is it real or virtual?

Answer 1

ho = height of object (brush)
f = focal length
do = distance of object
di = dist of image
hi = height of image

ho = 5 cm do = 20 cm f = 40 cm

di = ? hi = ?

To determine the image distance, use the mirror equation

1/f = 1/do + 1/di
1/(40 cm) = 1/(20 cm) + 1/di

di = -40.0 cm

Height of image:

hi/ho = - di/do
hi /(5.0 cm) = - (-40.0 cm)/(20 cm)

hi = - (5.0 cm)

Answer 2

Solution The focal length of the concave mirror is, f -40cm The height of the object (mascara brush) is, h, -5cnm The distance of the object is, u= 20cm To find the location of image from the mirror equation, u V Lu VE lu (20) (40) 20-40 -40 cm Hence, the location of image is-40 cm To find the height of the image, from the magnification formula tl 40 20 -10 cm Hence, the height of the image is 10 cm Since, the height of the mage is positive means it's an upright image. Hence, the image is upright Since, the distance of the image is negative means it's a virtual image. Hence, the image is virtual