Advertisements
Advertisements
Question
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.
Advertisements
Solution
From lens maker formula, we have
\[P = (\mu - 1)\left( \frac{1}{R_1} - \frac{1}{R_2} \right)\]
\[\text { where} \]
\[ P =\text { Power of lens } = + 5 D\]
\[\mu = \text { Refractive index of the lens } = 1 . 55\]
\[ R_1 =\text { Radius of curvature of first face } \left( + ve \right)\]
\[ R_2 = \text { Radius of curvature of second face } \left( - ve \right)\]
\[\text {Given }: \]
\[ R_1 = R_2 = R\]
\[ \Rightarrow P = (\mu - 1)\left( \frac{1}{R_1} - \frac{1}{R_2} \right)\]
\[ \Rightarrow 5 = (1 . 55 - 1)\left( \frac{1}{R} - \frac{1}{- R} \right)\]
\[ \Rightarrow 5 = (1 . 55 - 1)\left( \frac{2}{R} \right)\]
\[ \Rightarrow 5 = 0 . 55\left( \frac{2}{R} \right)\]
\[ \Rightarrow R = \frac{0 . 55 \times 2}{5}\]
\[ \Rightarrow R = 0 . 22 m\]
APPEARS IN
RELATED QUESTIONS
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?
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.
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?
Two concave lenses L1 and L2 are kept in contact with each other. If the space between the two lenses is filled with a material of smaller refractive index, the magnitude of the focal length of the combination
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.
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.
An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus. The image ______.
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.
