Q#1
Is the formula "Real depth/Apparent depth = µ" valid if viewed from a position quite away from the normal?ANSWER:
No. Because in its derivation the formula
Sin i/sin r = µ
has been used and keeping the angles i and r very small, the approximation sin i ≈ tan i, and sin r ≈ tan r have been taken. When viewed from a position quite away from the normal these approximations do not hold good. Hence the formula "Real depth/ Apparent depth = µ" is not valid.
Q#2
Can you ever have a situation in which a light ray goes undeviated through a prism?
ANSWER:
If the light ray falls perpendicularly on the surface and the angle of the prism is zero, i.e.
I = i' = A =0
ẟ = I + i'- A = 0
But in this case the sides of the prism are parallel and we may not call it a prism practically because it will look like a cuboid.
Another case is when the prism is submerged in a dense liquid which refractive index is the same as the prism. Since the speed of light will not change in both medium hence the light will travel undeviated through the prism.
Q#3
Why does a diamond shine more than a glass piece cut to the same shape?
ANSWER:
There are two reasons. First, due to the higher refractive index, the critical angle for diamond is less and the light goes a larger number of total internal reflections inside the diamond than the glass.
Second, there is more variation of µ between violet and red light for the diamond than the glass. Hence the dispersion is wider in diamond than the glass.
These two reasons combined make the diamond more shiny and sparkling.
Q#4
A narrow beam of light passes through a slab obliquely and is then received by an eye (figure 18-Q1). The index of refraction of the material in the slab fluctuates slowly with time. How will it appear to the eye? The twinkling of stars has a similar explanation.
ANSWER:
When the index of refraction, µ changes the refracted rays in the slab change its direction. Thus they emerge out of the slab at different points. This results in the shift of the image of the source and the eye find the source disappearing/shifting a bit with time and the source appears twinkling like a star.
Q#5
Can a plane mirror ever form a real image?
ANSWER:
Generally a plane mirror does not form a real image because the light coming from real objects diverge after reflection from the plane mirror. But consider a situation of convex lens or concave mirror where a real image is forming, if the plane mirror is placed between the image and the lens/mirror, the incident rays after reflection form a real image at a different place.
Q#6
If a piece of paper is placed at the position of a virtual image of a strong light source, will the paper burn after sufficient time? What happens if the image is real? What happens if the image is real but the source is virtual?
ANSWER:
No, at the position of the virtual image, light rays do not actually converge, hence the piece of paper will not be affected.
Yes, if the image is real the paper will burn after sufficient time. For example, a convex lens can be used to form a real image of the sun at its focal point. If a piece of paper is put at this point it will burn. This technique was used to make a fire long ago.
Yes, since the image is real, the light rays actually converge at the point.
Q#7
Can a virtual image be photographed by a camera?
ANSWER:
If the virtual image is taken as a virtual object, it can be photographed by a camera because of the camera photographs the real image formed at its plate or screen. The virtual objects can have real images.
But a virtual image can not make an impression on a photographic plate placed at this position due to the fact that virtual images cannot be projected on a screen.
Q#8
In motor vehicles, a convex mirror is attached near the driver's seat to give him the view of the traffic behind. What is the special function of this convex mirror which a plane mirror cannot do?
ANSWER:
A convex mirror forms a virtual, erect and diminished image behind the mirror if the object is in front of it. So it covers a vast area behind the driver.
The plane mirror also forms virtual and erect image behind the mirror but it is of the same size. So the plane mirror does not cover a wide field behind the driver. Hence the convex mirror is used.
Q#9
If an object far away from a convex mirror moves towards the mirror, the image also moves. Does it move faster, slower or at the same speed as compared to the object?
ANSWER:
If the object is far away from a convex mirror the virtual image is near the focus. As the object moves towards the mirror the image moves towards the back of the mirror. So in an equal interval of time, the object moves a larger distance than the image. So the image moves slower than the object.
Q#10
Suppose you are inside the water in a swimming pool near an edge. A friend is standing on the edge. Do you find your friend taller or shorter than his usual height?
ANSWER:
Let the friend's height be AB. The ray from top AO enters the water at O and bends towards the normal at O. The refracted ray OC travels to the eye at C. The eye perceives the ray coming from A' which is the virtual image of A on the extended line CO. Thus the friend's height seems A'B instead of AB. A'B is taller than AB.
So the friend will appear taller than usual.
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