the image formed by a spherical mirror is real inverted and is of magnification -2.If the image is formed at a distance of 30cm from the mirror , where is the object placed ? Find the focal length of the mirror . list two characteristics of the image formed if the object is moved 10cm towards the mirror.
Answers
Since the spherical mirror forms an real, inverted and magnified (2>1) image, the spherical mirror is concave. The two cases in which a concave mirror forms a real inverted magnified image is when the object is at focus and image is at infinity and when the object is between center of curvature and focus and image is formed beyond center of curvature. Clearly, the image is not at infinity. Therefore, the object is between C and F. The object distance is -v/u.
Magnification=-v/u
-2=30/u
u=-15
By mirror formula,
1/v+1/u=1/f
1/-30 + 1/-15=1/f
1/f= 1+2/-30= 3/-30
f=-10 cm
If the object is moved towards the F then image is formed at infinity and the nature of the image is real, inverted, highly magnified
Answer:
Given :
Magnification m = - 2
Image distance v = 30 cm
We know :
m = - v / u
- 2 = - (- 30 ) / u
u = - 15 cm
We have mirror formula :
1 / f = 1 / v + 1 / u
1 / f = 1 / - 15 - 1 / 30
1 / f = - 1 / 10
f = - 10 cm
When the object is moved 10 cm towards the mirror.
Then : u' = u - 10 cm
= > u' = - 5 cm
Again putting in formula to get v'
1 / - 10 + 1 / 5 = 1 / v'
1 / v' = 2 - 1 / 10
v' = 10 cm
Therefore , the image is located 10 cm behind the mirror.
Also new magnification :
m' = -v' / u'
m' = - 10 / -5
m' = 2
Since magnification is positive the image is erect and virtual.
Also image is magnified in nature.