Light : Reflection And Refraction - 1

If the lower half (or a part) of a mirror is covered with a black paper then a complete image of the object will be formed as before. However, the image will be less bright now.

Here, ∠i = 60°, ∠r = 45°
Using Snell’s law of refraction, refractive index of medium B with respect to medium A.

A full length image of a distant tall building can definitely be seen by using a convex mirror because a convex mirror always forms a virtual, erect and highly diminished image.

The angle of incidence of any light ray passing through the centre of curvature of a spherical mirror is 0°, because a line joining centre of curvature to any point on the mirror is a normal drawn at that point of the mirror.

Given h₀ = +10 mm - + 0.1 cm 
h₂ = - 5 mm = -0 .5 cm
for real image, v = - 30 cm                       

Now magnification,

∴ f = -20 cm

Magnification is negative for a real and inverted image formed by a mirror.

Parallel rays after refracting meet at the focus of a convex lens.

As light rays from sun (u = ∞) converge at a point 15 cm in front of a concave mirror, hence focal length of concave mirror f = - 15 cm.
To form an image of exactly same size as that of an object, the object should be placed at the centre of curvature (u = R = 2f) of mirror. Hence, the object should be placed at 30 cm in front of mirror.

To get the real and magnified image for a convex lens, the object is placed in between F and 2F.

A concave mirror forms a virtual, erect and magnified image when an object is placed between pole and focus point of the mirror. As focal length of given concave mirror, hence object must be placed at a distance less than 12 cm i.e., u < 12 cm. Thus, the object may be placed at a distance of 10 cm from the mirror.