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.

When object is at 2F, real inverted and same size image is formed by convex lens. So, according to question option (a) and (b) both are correct.

Image when object placed between F and 2F:-

Image when object is placed at 2F, which is of same size as that of object.

Image formed when object is at focus of the convex lens:-

When the object is placed at the first principal focus, the image is formed at infinity and the image is real, inverted and infinitely large.

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.