The radius of curvature of a concave spherical mirror is 33.5 cm. (Make sure to

Question

The radius of curvature of a concave spherical mirror is 33.5 cm. (Make sure to use the appropriate sign in your final answers.) (a) Find the image distance and magnification if an object is placed 75.5 cm in front of the mirror?

di = ___________cm

M = ________________

Is this image real or virtual?

real

virtual    

Is it upright or inverted?

upright

inverted    

(b) Find the image distance and magnification if an object is placed 33.5 cm in front of the same mirror?

di =_______________ cm

M =__________________ Is this image real or virtual? real virtual   

Is it upright or inverted? upright inverted  

Explanation / Answer

The focal length of the mirror is

f = radius of curvature / 2 = 33.5 cm /2 = 16.75 cm

a) The image distance (di ) can be find out by using

1/f = (1/di ) + (1/do ) {do = Object distance from mirror = 75.5 cm }

di = ( f do ) / (do - f )

di = [ (16.75cm) (75.5 cm) ] / [75.5 cm - 16.75 cm]

di = + 21.53 cm

Here +ve sign indicates the image formed is real.

Magnification (m) = - di / do = - (21.53 cm ) / (75.5 cm) = - 0.2852

Here -ve sign indicates the image is inverted.

b) In this case the object distance changed to di =33.5 cm then from the mirror equation

1/f = (1/di ) + (1/do ) {do = Object distance from mirror = 33.5 cm }

di = ( f do ) / (do - f )

di = [ (16.75cm) (33.5 cm) ] / [33.5 cm - 16.75 cm]

di =+33.5 cm (Image is formed at the object position )

Here +ve sign indicates the image formed is real.

Magnification (m) = - di / do = - (33.5 cm ) / (33.5 cm) = - 1.0 (Image is with the same size of object )

Here -ve sign indicates the image is inverted.

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