Question

Draw the ray diagram to show the formation of an image when a real object is placed in front of a spherical mirror in such a way that the magnification image produced by the mirror is -1.

Answer 1

Magnification of image is the ratio of the height of the image to the height of the object and it is denoted by m and when image is virtual the height should be taken positive and when image is real height should be taken as negative.
Formula used:
$m=\dfrac{h}{h'}$

Complete answer:
$\to$ Here in the question it is given that magnification is -1 that means the height of the object ($h'$) and height of the image will be equal.
$\to$ Now the negative magnitude of the image indicates that the image produced by the mirror is a real and inverted image.
$\to$ Now in a concave mirror image produced is a real image means it is in front of the mirror and it is inverted.
$\to$ When we put object at the center of the curvature at mirror image is produced will have same height as real object and the image will be inverted so height will be negative, hence
$m=\dfrac{h}{h'}$
m = magnification
h = height of the mirror image
$h'$ = height of the real object.

& m=\dfrac{h}{-h}\text{ }\left( \because -h'=h \right) \\\ & m=-1 \\\ \end{aligned}$$ Figure of the ray diagram.  **Additional information:** Spherical mirror: - Spherical mirrors are the mirrors having curved surfaces that are painted on one of their sides. Concave mirror: - Spherical mirrors in which outward surfaces are painted are known as concave mirrors. Concave mirrors are also known as converging mirrors. Convex mirror: - Spherical mirrors in which inward surfaces are painted are known as concave mirrors. Convex mirrors are known as diverging mirrors. **Note:** There are two types of mirrors one is convex and other one is concave and convex mirror the image will be virtual, erect and demised and whether in the concave mirror the image will be real and inverted but when it is inside the focal point (f) then the image will be virtual and erect.