An object is p = 34.3 cm in front of a concave mirror. Its real image height is 6 times larger than the object height.
What is the location of the image?
Answer in units of cm.
What is the radius of curvature of the mirror? Answer in units of cm.
To answer this question, we can use the mirror formula and the magnification formula for concave mirrors.
The mirror formula is given by:
1/f = 1/v - 1/u
where:
f is the focal length of the mirror,
v is the image distance, and
u is the object distance.
The magnification formula is given by:
m = -v/u
where:
m is the magnification.
Let's solve for the image distance first. We are given that the object distance (u) is 34.3 cm and the magnification (m) is 6. We can use the magnification formula to find the image distance (v):
6 = -v/34.3
Multiplying both sides by 34.3, we get:
-204.8 = v
Therefore, the image distance (v) is -204.8 cm.
Next, let's find the focal length (f) of the mirror. We can rearrange the mirror formula to solve for f:
1/f = 1/v - 1/u
Substituting the values, we get:
1/f = 1/(-204.8) - 1/34.3
Simplifying, we have:
1/f = -0.00488 - 0.02917
Adding the two fractions, we get:
1/f = -0.03405
Taking the reciprocal of both sides, we find:
f = -29.37 cm
Therefore, the focal length (f) of the mirror is -29.37 cm.
Lastly, we can find the radius of curvature (R) of the mirror using the relation:
R = 2f
Substituting the focal length we just calculated, we get:
R = 2*(-29.37) = -58.74 cm
Therefore, the radius of curvature (R) of the mirror is -58.74 cm.
Note: The negative signs indicate that the mirror is concave.