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Question: Converging rays strike a spherical convex mirror such that they can form the image in the absence of...

Converging rays strike a spherical convex mirror such that they can form the image in the absence of a mirror between pole and focus. Which of the following is a characteristic of the final image formed by the mirror?

A. Real
B. Virtual
C. Erect
D. Inverted

Explanation

Solution

In this solution, observing the object as virtual, then using mirror formula and find the magnification out of it.

Complete step by step solution:
Here, we observed that object is virtual. So the object distance is positive.
From mirror formula,
1v+1u=1f\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}
1v=−1u+1f\dfrac{1}{v} = - \dfrac{1}{u} + \dfrac{1}{f}

v<0v < 0
On the left of the mirror, the image is created and thus it’s virtual.
A spherical mirror magnification is given by:
m=−vu>0m = \dfrac{{ - v}}{u} > 0

Hence, it is erect, Options B and C are correct.

Additional information:

Converging rays: If reflected rays converge after reflecting to a single point, it is called a converging mirror behavior. This is seen by the creation of a real picture. This can be used in applications in which all light intensity is concentrated at a time.

Spherical convex mirror (Curved mirror): A curved mirror is a reflection surface mirror. It may be convex (externally bolting) or concave (inwardly recessed). The surfaces of most curved mirrors are shaped like a part of a sphere, but in optical instruments, another form is often used. Parabolic reflectors, used in optical devices such as telescopes to view distant objects, are the most common non-spherical type since spherical mirror structures, including spherical lenses, suffer from spherical aberrations. For fun, distorting mirrors are used.

Mirror formula: It's an equation that applies to object distance and the focal length of the image are called a mirror equation. It is also called the composition of a mirror. In a spherical mirror: a focus length (f) is the distance from the main focus and the pole of the mirror.
Concave mirror: 1F=1U+1V\dfrac{1}{F} = \dfrac{1}{U} + \dfrac{1}{V}
Convex mirror: 1U−1V=−1F\dfrac{1}{U} - \dfrac{1}{V} = \dfrac{{ - 1}}{F}

Note: The image distance should be taken less than zero. By taking more than zero it may affect the result. Use proper mirror formula which is 1v+1u=1f\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}.