Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +16 cm, the type of mirror is concave, and then the distance between the focal point and the mirror is 11 cm (without proper sign).

Find :

(a) the radius of curvature r (including sign),

(b) the image distance i, and

(c) the lateral magnification m. Also, determine whether the image is

(d) real or virtual ,

(e) inverted from object O or non inverted , and

(f) on the same side of the mirror as O or on the opposite side.

a

The radius of curvature is

b

the image distance

c

the lateral magnification is

d

The image is real given that the object distance is greater than the focal length and this is a type of setup that gives a real image in concave mirror

e

This would be inverted because from above we see that the image is real and all real image are inverted i concave mirror

f

This image would be on the same side of the object this is because both the image distance and the object distance are positive

Explanation:

From the question we are told that

                 The object distance is  

                  The focal length is  

The focal length is mathematically given as

   Where R is the radius of curvature

Now making R the subject of the formula above

                  (the positive sign is because it is in the real world size)

The mathematical representation of the mirror formula is

Mathematically  lateral magnification is represented as

Where I is the image distance and u is the object distance

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