In an experiment a convex lens of focal length 15cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5cm from it. It is found that an object and it’s image coincide, if the object is placed at a distance of 20cm from the lens. The focal length of the convex mirror is:A. 27.5 cmB. 20.0 cmC. 25.0 cmD. 30.5 cm

To find the focal length of the convex mirror in this setup, we can use the mirror formula, which relates the object distance (u), the image distance (v), and the focal length (f) of the mirror. The mirror formula is given by:

1/f = 1/v + 1/u

Where:

f is the focal length of the mirror (which we want to find).
v is the image distance (the distance from the mirror to the image formed by the mirror).
u is the object distance (the distance from the mirror to the object).
In this case, the lens and the mirror are coaxial, which means they share the same optical axis. When the object and its image coincide, the image distance (v) is zero. So, we have:

1/f = 1/0 + 1/u

Since 1/0 is undefined, this means that the object distance (u) must be equal to the focal length of the convex lens (15 cm):

u = 15 cm

Now, we can plug this value of u into the mirror formula:

1/f = 1/0 + 1/15

Since 1/0 is undefined, we ignore it, and we are left with:

1/f = 1/15

Now, solve for f:

f = 15 cm

So, the focal length of the convex mirror is 15 cm. Therefore, the correct answer is not among the options provided.