Question

What sign \[(+ve\And -ve)\]has been given to the following on the basis of Cartesian Sign Convention?
A. Height of real image
B. Height of virtual image

Answer 1

Hint: Since sign convention as taken as coordinate system. Like the left side of origin is taken as negative, the right side is taken as positive. Upper region is taken as positive and the lower region is taken as negative. So the same logic is applied for optics in taking sign considerations for mathematical purposes.

Complete step-by-step solution:
Real image is always obtained on screen and virtual image is always obtained behind screen.
For real image it is always inverted and virtual image is always erect either it is mirror or lens.
According to Cartesian sign convention, distance of object is always taken as negative for any lens or mirror. This is because the object distance is always measured against the direction of incident light.
For mirrors,
Real image is always obtained by Concave Mirrors and on the same side of the object and it is always inverted so height of real image is always taken as\[-ve\].
Virtual image is obtained by Convex Mirrors and on the back side of the object and it is always erect so height of virtual image is taken as\[+ve\]sign.
For lenses
Real image is always obtained by convex lens or converging lens and on the other side of the object it is always inverted so height of real image is always taken as\[-ve\]sign. Only in one case when an object is placed anywhere between focal point and optical centre then it forms a virtual image but erect so that sign is taken as \[+ve\]sign.

Virtual image is obtained by concave lens or diverging lens and on the same side of object and it is always erect so height of virtual image is taken as\[+ve\]sign.
So, we can conclude that Concave Mirror and Convex lenses form real images with \[-ve\] sign and Convex Mirror and Concave Lens form virtual images with \[+ve\] sign.

Note:Mirrors are based on the phenomenon of reflection and mirrors are classified as Plane mirror and Spherical mirrors. These Convex and Concave mirrors come in the spherical mirror category. Lenses are based on the phenomenon of refraction and just like mirror lenses are also classified are Plane glass and Spherical lenses. These Convex and Concave lens comes in spherical lenses categ