Advertisements
Advertisements
प्रश्न
Figure shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?
Advertisements
उत्तर
Focal length of the convex lens, f1 = 30 cm
The liquid acts as a mirror. Focal length of the liquid = f2
Focal length of the system (convex lens + liquid), f = 45 cm
For a pair of optical systems placed in contact, the equivalent focal length is given as:
`1/"f" = 1/"f"_1 + 1/"f"_2`
`1/"f"_2 = 1/"f" - 1/"f"_1`
= `1/45 - 1/30`
= `-1/90`
∴ f2 = −90 cm
Let the refractive index of the lens be μ1 and the radius of curvature of one surface be R. Hence, the radius of curvature of the other surface is −R.
R can be obtained using the relation:
`1/"f"_1 = (μ_1 - 1)(1/"R" + 1/(-"R"))`
`1/30 = (1.5 - 1) (2/"R")`
R = `30/(0.5 xx 2)`
∴ R = 30 cm
Let μ2 be the refractive index of the liquid.
Radius of curvature of the liquid on the side of the plane mirror = ∞
Radius of curvature of the liquid on the side of the lens, R = −30 cm
The value of μ2 can be calculated using the relation:
`1/"f"_2 = (μ_2 - 1)[1/(-"R") - 1/∞]`
`(-1)/90 = (μ_2 - 1)[1/(+30) - 0]`
`μ_2 - 1 = 1/3`
μ2 = `1/3 + 1`
μ2 = `4/3`
∴ μ2 = 1.33
Hence, the refractive index of the liquid is 1.33.
APPEARS IN
संबंधित प्रश्न
You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.
The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3 m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?
An object 1.5 cm in size is placed on the side of the convex lens in the arrangement (a) above. The distance between the object and the convex lens is 40 cm. Determine the magnification produced by the two-lens system, and the size of the image
A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm.
(a) What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?
(b) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?
A card sheet divided into squares each of size 1 mm2 is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 cm) held close to the eye.
- What is the magnification produced by the lens? How much is the area of each square in the virtual image?
- What is the angular magnification (magnifying power) of the lens?
- Is the magnification in (a) equal to the magnifying power in (b)? Explain.
An equiconvex lens of focal length 'f' is cut into two identical plane convex lenses. How will the power of each part be related to the focal length of the original lens ?
A double convex lens of + 5 D is made of glass of refractive index 1.55 with both faces of equal radii of curvature. Find the value of its radius of curvature.
Two converging lenses of unequal focal lengths can be used to reduce the aperture of a parallel beam of light without loosing the energy of the light. This increase the intensity. Describe how the converging lenses should be placed to do this.
A convex lens forms a real image of a point object placed on its principals axis. If the upper half of the lens is painted black,
(a) the image will be shifted downward
(b) the image will be shifted upward
(c) the image will not be shifted
(d) the intensity of the image will decrease.
A small piece of wood is floating on the surface of a 2.5 m deep lake. Where does the shadow form on the bottom when the sum is just setting? Refractive index of water = 4/3.
A pin of length 2.0 cm lies along the principal axis of a converging lens, the centre being at a distance of 11 cm from the lens. The focal length of the lens is 6 cm. Find the size of the image.
Answer the following question.
An optical instrument uses a lens of 100 D for the objective lens and 50 D for its eyepiece. When the tube length is kept at 20 cm, the final image is formed at infinity.
(a) Identify the optical instrument.
(b) Calculate the magnification produced by the instrument.
Will the focal length of a lens for red light be more, same or less than that for blue light?
An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed?
In many experimental set-ups the source and screen are fixed at a distance say D and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points.
A plano convex lens has diameter of 10 cm and its thickness at the centre is 0.5 cm. Speed of light in the lens is 2 × 108 ms-1. What is the focal length of the lens?
Show that the least possible distance between an object and its real image in a convex lens is 4f, where f is the focal length of the lens.
