The radius of curvature of a concave spherical mirror is 28.5 cm. (Make sure to

Question

The radius of curvature of a concave spherical mirror is 28.5 cm. (Make sure to use the appropriate sign in your final answers.)

(a) Find the image distance and magnification if an object is placed 73.5 cm in front of the mirror?

di =

M =

Is this image real or virtual?

realvirtual    

Is it upright or inverted?

uprightinverted    

(b) Find the image distance and magnification if an object is placed 28.5 cm in front of the same mirror?

di =

M =

Is this image real or virtual?

realvirtual    

Is it upright or inverted?

uprightinverted   

di =

M =

Explanation / Answer

Given that

radius of curvature R=28.5 cm

focal length of spherical mirror f=28.5/2=14.25 cm

now we find the image distance object is placed at 73.5 cm

1/v+1/u=1/f

1/v+1/73.5=1/14.25

1/v=1/14.25-1/73.5

1/v=73.5-14.25/14.25*73.5

v=1047.4/59.25=17.7 cm

now we find the magnifaction

magnifaction m=v/u=17.7/73.5=0.241

the image is real and upright

----------------------------------------------------------------------------------------------------------------------------

now we find the image distance at object is placed 28.5 cm

1/v+1/u=1/f

1/v+1/28.5=1/14.25

1/v=1/14.25-1/28.5

image distance v=28.5*14.25/28.5-14.25

=28.5 cm

magnifaction m=28.5/28.5=1

the image is real and uprightinverted

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