Question

Find the distance of the object from concave mirror of focal length 50 so that image size 4 times the size of object

Answer 1

Explanation:

Spherical mirror object and image positions fulfill Descartes´ Equation:

1/x + 1/x´= 1/f Equation 1

x is the abscissa of the object. x´is the abscissa of the image (our incognita), f is the focal length of the mirror and c is the abscissa of the center of curvature. Notice the I use abscissas instead of distances (abscissas can be negative while distances not).

In our case f=10 cm.

We want to find an inverted image of 5 times the size of the object. That is, we want a lateral magnification m=-5.

Lateral magnification in spherical mirrors equals m= - x´/x (Equation 2) and that should be equal to -5.

So, we have two equations (1 and 2) and two unknowns: x and x´.

Solving for x and x´:

x=12 cm and x´= 60 cm