How to Calculate Image Location and Magnification for a Concave Spherical Mirror
Calculating Image Location and Magnification for Concave Spherical Mirror
(a) For an object distance of 27.8 cm, the image is located approximately 18.56 cm from the mirror, and the magnification is approximately -0.67.
(b) For an object distance of 11.1 cm, the image is located approximately 18.56 cm from the mirror, and the magnification is approximately -1.67.
To solve this problem, we can use the mirror formula:
1/f = 1/u + 1/v
Where f is the focal length, u is the object distance, and v is the image distance.
Calculations:
(a) For an object distance of 27.8 cm:
Substitute the values into the mirror formula:
1/11.1 = 1/27.8 + 1/v
Rearrange the equation to solve for v:
1/v = 1/11.1 - 1/27.8
v ≈ 18.56 cm
Magnification (M) ≈ -0.67
(b) For an object distance of 11.1 cm:
1/v = 1/11.1 - 1/27.8
v ≈ 18.56 cm
M ≈ -1.67
Therefore, for an object distance of 27.8 cm, the image is located approximately 18.56 cm from the mirror with a magnification of approximately -0.67. For an object distance of 11.1 cm, the image is also located approximately 18.56 cm from the mirror with a magnification of approximately -1.67.