the inverted image of a light bulb is formed on a screen located 9 metres from spherical mirror.the image is 4 times larger than the light bulb.determine the object distance
To determine the object distance, we can use the mirror equation, which is given by:
1/f = 1/u + 1/v
where f is the focal length of the mirror, u is the object distance, and v is the image distance.
Given that the image is 4 times larger than the light bulb, we know that the magnification (m) is equal to -4. Magnification is given by:
m = -v/u
Rearranging the magnification equation, we have:
v = -4u
Substituting this value for v in the mirror equation, we have:
1/f = 1/u + 1/(-4u)
Simplifying further:
1/f = (1-4)/(-4u)
1/f = -3/(-4u)
Cross-multiplying:
-4uf = -3
Simplifying:
uf = 3/4
Therefore, the object distance (u) is equal to 3/4, or 0.75 meters.