A concave mirror having a radius of curvature 40 cm is placed in front of an illuminated point source at a distance of 30 cm from it.Find the location of the image.
I got 6cm as my answer and its wrong
C at 40
F at 20
object at 30, halfway between C and F
so
image is BEYOND C
http://www.physicsclassroom.com/class/refln/Lesson-3/Image-Characteristics-for-Concave-Mirrors
1/f = 1/do + 1/di
1/20 = 1/30 + 1/di
60/20 = 60/30 + 60/di
3 = 2 + 60/di
di = 60 cm
To find the location of the image formed by a concave mirror, we can use the mirror equation:
1/f = 1/v - 1/u
where:
f is the focal length of the mirror,
v is the distance of the image from the mirror, and
u is the distance of the object from the mirror.
Given data:
Radius of curvature (R) = 40 cm
Distance of the object (u) = -30 cm (negative sign represents object placed in front of the mirror)
To find the focal length (f), we can use the formula:
f = R / 2
Substituting the given value:
f = 40 / 2 = 20 cm
Now, we can substitute the values of f and u into the mirror equation:
1/20 = 1/v - 1/-30
Simplifying this equation, we get:
1/v = 1/20 + 1/30
To combine the fractions with a common denominator, we can multiply both the numerator and denominator of each fraction by the least common multiple (LCM) of 20 and 30, which is 60:
1/v = (3/60) + (2/60)
= 5/60
= 1/12
Taking the reciprocal of both sides, we find:
v = 12 cm
The location of the image formed by the concave mirror is 12 cm away from the mirror.
Therefore, the correct answer is 12 cm, not 6 cm.