Solved Problems of Spherical Mirrors

In previous classes, we already covered all the theory related to plane and spherical mirrors, and examples of reasoning with plane mirrors were also shown. Now it is time to review some solved problems with spherical mirrors. Below, we will review some typical problems about spherical mirrors and their step-by-step solutions.

Spherical Mirror Problems

1. An object of 20[cm] is 1.5[m] away from a concave mirror. If the radius of curvature is 70[cm], calculate:
   1. The position of the reflected object and determine if it is real or virtual.
   2. The magnification factor and the orientation of the reflected object.
   3. The size of the reflected object.
2. An object of 10[cm] is placed 5[cm] away from a convex mirror with a radius of curvature of 12[cm]. Calculate:
   1. The position of the reflected object and determine if the image is virtual or real.
   2. The magnification factor and orientation of the image.
   3. The size of the reflected object.
3. A concave mirror with a radius of curvature of 12[cm] is given. Find the places where, if an object is placed, its image will double its size and determine if such an image is real or virtual.
4. Is it possible to magnify the image of an object using a convex mirror?
5. A convex mirror with a radius of curvature of 80[cm] has a useful surface of 60°. Determine the size of the largest possible object that can be reflected in it if placed 30[cm] from the vertex of the mirror.

Solutions:

Problems: Movement in front of spherical mirrors

1. Consider a spherical mirror with a radius of curvature R=70[cm]. If an object moves at a speed v=5[m/s], at what speed will its image move? Assume the position of the object is s=150[cm].
2. Consider a convex mirror with a radius of curvature R=-80[cm], and an object with a position S=10[cm]. If the mirror moves at a speed v=5[km/h], at what speed does the image move?
3. Consider a convex mirror with a radius of curvature R=-150[cm]. If a ball is at a position S=20[cm] and falls from rest from a height h=50[cm], find a formula that describes the speed at which the ball’s image falls in the mirror.

Solutions: