Test: Reflection through Spherical surfaces(26 Dec) - JEE MCQ

for concave mirror u=−7.5 ; f=−5
(1/v)+1/u=1/f
1/v-2/15=-1/5
i.e, image formed at pole of convex mirror for convex mirror, u=0;f=+5
(1/v)+1/u=1/f
(1/v)+1/0=1/5
V=0
So the final image is formed on a pole of a convex mirror.

When the object is placed at principal focus (F) of a concave mirror, a highly enlarged image is formed at infinity.

Focal length in air = 20 cm
Refractive index of air-water n₁= 1.33
Refractive index of air - glass n₂= 1.5
For focal length in air,
Using formula of lens
1/f_air={(n₂/n₁)-1}(1/R₁)-(1/R₂)
Put the value into the formula
1/20={(1.5/1)-1}{(1/R₁)-(1/R₂)}
1/20=0.5{(1/R₁)-(1/R₂)}…1
We need to calculate the focal length in water
Using formula of lens
1/f_water={(1.5/1.33)-1}{(1/R₁)-(1/R₂)}
1/f_water=0.128{(1/R₁)-(1/R₂)}….2
f_water/20=0.5/0.128
f_water=78.125cm

If a hollow sphere is cut into parts and the outer surface of the cut part is painted. Then it becomes a mirror with its inner surface as the reflecting surface This kind of mirror is known as concave mirror. Light converges at a point when it strikes and reflects back from the reflecting surface of concave mirror. Hence, it is also known as converging mirror.  When concave mirror is placed very close to the object, a magnified and virtual image is obtained. But if we increase the distance between the object and the mirror then the size of the image reduces and a real image is formed. So the image formed by concave mirror can be small or large and it can also be real or virtual.

A real image is defined as one that is formed when rays of light are directed in a fixed point.  A real image can be projected or seen on a screen. The best example of a real image is the one formed on a cinema screen.
A virtual image is defined as the opposite of a real image, therefore an image that cannot be obtained on a screen is referred to as a virtual image. The explanation for this is the fact that the rays of light that form a virtual image never converge therefore a virtual image can never be projected onto a screen. The best example of a virtual image is your reflection in the mirror.
Real images are produced by intersecting rays while virtual images are produced by diverging rays.
Real images can be projected on a screen while virtual ones cannot.
Real images are formed by two opposite lenses, concave and convex.
Virtual images are always upright while real images are always inverted.
 

A convex mirror is sometimes referred to as a diverging mirror due to the fact that incident light originates from the same point and will reflect off the mirror surface and diverge. The diagram at the right shows four incident rays originating from a point and incident towards a convex mirror.

A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century, by Isaac Newton, as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives.
Astronomical (reflecting) telescopes. In a reflecting telescope, instead of a convex objective lens, a concave mirror is used to collect parallel rays from the object and form an image at the focal point. Then the convex eyepiece lens is used to magnify this image for the viewer.
 

The power of a lens is the reciprocal of the focal length with measurement in metres. The unit is diopter.

It is given that the focal length of a convex lens is 10 cm = 0.1 m.

⇒ The power of the lens is 1/0.1= 10 diopter.

In a concave mirror when the object is located beyond C the magnification is less than one as the image formed is smaller than the object.

Only Convex Mirror can form an image which is upright and reduced in size.