Question

The radius of curvature of a convex spherical mirror is 1.5 m. How far away from the mirror is an object of height 12 cm. If the distance between its virtual image and the mirror is 0.35 m? What is the height of the image?

Answer 1

Hint: We know that suppose an object is placed u cm in front of a spherical mirror of focal length f such that the image is formed v cm from the mirror, then u, v and f are related by the equation; 1/f= 1/u + 1/v. This equation is referred to as the mirror formula. The formula holds for both concave and convex mirrors. It is an equation relating object distance and image distance with focal length is known as a mirror equation. It is also known as a mirror formula. In a spherical mirror: The distance between the principal focus and pole of the mirror is called Focal Length(f). Using this concept, we have to solve this question.

Complete step-by step answer:
It is known to us that the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.
Since, the radius of curvature is 1.2 m i.e., 120cm.
Therefore, focal length = -60 cm
From mirror formula is,
$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$
$\Rightarrow \dfrac{1}{-35}+\dfrac{1}{u}=\dfrac{1}{-60}$
$\Rightarrow \dfrac{1}{u}=\dfrac{1}{35}-\dfrac{1}{60}$
$\Rightarrow \dfrac{1}{u}=\dfrac{12-7}{420}$
$\Rightarrow u=84cm$
Image height $=\dfrac{12}{84}\times 35=5cm$
Thus, image height will be 5cm.

 Hence, the answer is 5cm.

 Note: It should be known to us that radius refers to the distance between the center of a circle or any other point on the circumference of the circle and surface of the sphere. While on the other hand, the radius of curvature is the radius of the circle that touches the curve at a given point. A spherical lens or mirror surface has a center of curvature located either along or decentred from the system local optical axis. The vertex of the lens surface is located on the local optical axis. The distance from the vertex to the center of curvature is the radius of curvature of the surface.
It should be known to us that If the reflecting surface is the outer side of the sphere, the mirror is called a convex mirror. If the inside surface is the reflecting surface, it is called a concave mirror. Virtual images are always formed by convex mirrors and are formed by concave mirrors.