Q16 of 51 Page 345

A small pin fixed on a table top is viewed from above from a distance of 50cm. By what distance would the pin appear to be raised if it is viewed from the same point through a 15cm thick glass slab held parallel to the table? Refractive index of glass = 1.5. Does the answer depend on the location of the slab?

Given:


Actual depth of the pin, d = 15 cm
Let apparent depth of the pin = d’ cm
Refractive index of glass, μ = 1.5



Ratio of actual depth to the apparent depth is equal to the refractive index of glass,
i.e.


μ = d / d′


⇒ d’ = d × μ


⇒ d’ = 15 × 1.5 = 10cm


The distance at which the pin appears to be raised D,


D = d’-d


D = 15-10 = 5cm


So the pin appears to be raised by 5 cm.
For a small angle of incidence, this distance does not depend upon the location of the slab.


More from this chapter

All 51 →
14

(a) A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0cm is used, what is the angular magnification of the telescope?

(b) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 106m, and the radius of lunar orbit is 3.8 × 108m.

 15

Use the mirror equation to deduce that:

(a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.


(b) a convex mirror always produces a virtual image independent of the location of the object.


(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.


(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.


[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

 17

(a) Figure 9.35 shows a cross-section of a ‘light pipe’ made of a glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure.

(b) What is the answer if there is no outer covering of the pipe?


 18

Answer the following question:

You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.