Advertisements
Advertisements
प्रश्न
A small object is placed at the centre of the bottom of a cylindrical vessel of radius 3 cm and height 4 cm filled completely with water. Consider the ray leaving the vessel through a corner. Suppose this ray and the ray along the axis of the vessel are used to trace the image. Find the apparent depth of the image and the ratio of real depth to the apparent depth under the assumptions taken. Refractive index of water = 1.33.
Advertisements
उत्तर
Given,
Refractive index of water μ = 1.33
Radius of the cylindrical vessel = 3 cm
Height of the cylindrical vessel = 4 cm
Let x be the length of BD
According to the diagram,
\[\frac{x}{3} = cot r . . . . (i)\]
Using Snell's law,
\[\frac{\sin i}{\sin r} = \frac{1}{1 . 33} = \frac{3}{4}\]
\[ \Rightarrow \sin r = \frac{4}{3}\sin i = \frac{4}{3} \times \frac{3}{5} = \frac{4}{5}\]
\[As \sin i = \frac{BC}{AC} = \frac{3}{5}\]
\[ \Rightarrow \cot r = \frac{3}{4} . . . . . (ii)\]
From (i) and (ii),
\[\frac{x}{3} = \frac{3}{4}\]
\[ \Rightarrow x = \frac{9}{4} = 2 . 25 \text{ cm }\]
Hence, the ratio of real and apparent depth of the image will be \[4: 2 . 25 = 1 . 78\] 
APPEARS IN
संबंधित प्रश्न
Calculate the distance of an object of height h from a concave mirror of radius of curvature 20 cm, so as to obtain a real image of magnification 2. Find the location of the image also.
Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.
Use the mirror equation to deduce that the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
Use the mirror equation to deduce that an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.
A point object O is placed at a distance of 15cm from a convex lens L of focal length 1 Ocm as shown in Figure 5 below. On the other side of the lens, a convex mirror M is placed such that its distance from the lens is equal to the focal length of the lens. The final image formed by this combination is observed to coincide with the object O. Find the focal length of the convex mirror
Use the mirror equation to show that an object placed between f and 2f of a concave mirror forms an image beyond 2f.
Use the mirror equation to show a convex mirror always produces a virtual image independent of the location of the object ?
Can a plane mirror ever form a real image?
A point source of light is placed in front of a plane mirror.
following Figure shows two rays A and B being reflected by a mirror and going as A' and B'. The mirror
A light ray falling at an angle of 45° with the surface of a clean slab of ice of thickness 1.00 m is refracted into it at an angle of 30°. Calculate the time taken by the light rays to cross the slab. Speed of light in vacuum = 3 × 108 m s−1.
Name the physical principle on which the working of optical fibers is based.
For paraxial rays, show that the focal length of a spherical mirror is one-half of its radius of curvature.
A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is ______ mm.
The focal length f is related to the radius of curvature r of the spherical convex mirror by ______.
Car B overtakes car A at a relative speed of 40 ms-1. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car A, when car B is 1.9 m away from car A?
When a clock is viewed in a mirror, the needles exhibit a time which appears to be 8:20. Then the actual time will be:
Two plane mirrors are inclined at an angle of 40°. The possible number of images of an object placed at point P would be?
A point object is placed at a distance of 30 cm from a convex mirror of a focal length of 30 cm. What is the separation between the image and the object?
