Question A concave spherical mirror has a radius of curvature of 9.00 cm 1)Calcu
ID: 1443923 • Letter: Q
Question
Question A concave spherical mirror has a radius of curvature of 9.00 cm
1)Calculate the size of the image formed by an 8.00 mm -tall object whose distance from the mirror is 18.0 cm . in mm
2)Calculate the size of the image formed by an 8.00 mm -tall object whose distance from the mirror is 9.00 cm .in mm
3)Calculate the size of the image formed by an 8.00 mm -tall object whose distance from the mirror is 2.25 cm . in mm
4)Calculate the size of the image formed by an 8.00 mm -tall object whose distance from the mirror is 10.0 m . in mm
Explanation / Answer
radius of curvature=9cm so focal length=R/2=4.5cm
1)object distance=u=-18cm f=-4.5cm
using the relation 1/u+1/v=1/f
we have1/v=1/18-1/4.5 so v=-6cm and magnification =-v/u=-6/18=-1/3
so size of the image=size of the object X magnififcation=8X(-1/3)=-8/3mm the - sign shows that the image is inverted.
similarly b)
object distance=u=-9cm f=-4.5cm
using the relation 1/u+1/v=1/f
we have1/v=1/9-1/4.5 so v=-9cm and magnification =-v/u=-9/9=-1
so size of the image=size of the object X magnififcation=8X(-1)=-8mm the - sign shows that the image is inverted.
c)
object distance=u=-2.25cm f=-4.5cm
using the relation 1/u+1/v=1/f
we have1/v=1/2.25-1/4.5 so v=-2/9cm and magnification =-v/u=-2/9 X2/9=-4/81
so size of the image=size of the object X magnififcation=8X(-4/81)=-0.3950mm the - sign shows that the image is inverted.
d)
object distance=u=-1000cm f=-4.5cm
using the relation 1/u+1/v=1/f
we have1/v=1/1000-1/4.5 so v=-4.520cm and magnification =-v/u=-4.520 /1000=-4.520X10-3
so size of the image=size of the object X magnififcation=8X(-4.520X10-3)=-0.03616mm the - sign shows that the image is inverted.