Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is
- a convex lens of focal length 20 cm, and
- a concave lens of focal length 16 cm?
An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?
You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.
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 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.
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.
