You hold a spherical salad bowl 90 cm in front of your face

You hold a spherical salad bowl 90 cm in front of your face with the bottom of the bowl facing you. The salad bowl is made of polished metal with a 30 cm radius of curvature.

Where is the image of your 2.0cmtall nose located?

What is the image\'s size?

What is the orientation?

What is the nature (real or virtual)?

Solution

the object distance is p = 90 cm

focal length = 30/1 = - 15 cm

size of object = = 2cm

=> using mirror equation

1/f = 1/p + 1/q

q = -15*90)/(90-(-15)) =   -12.85 cm

=> m = -q/p = hi/ho

=> hi/2 = -(-12.85/90 )

=> hi = 2*(-12.85/90 ) = 0.285 cm

image distance is negative , so image formed behind the mirror

thus, image is virtual and magnification is positive , thus upright

therefore , image is virtual , upright and diminished