Advertisements
Advertisements
प्रश्न
A pin of length 2.00 cm is placed perpendicular to the principal axis of a converging lens. An inverted image of size 1.00 cm is formed at a distance of 40.0 cm from the pin. Find the focal length of the lens and its distance from the pin.
Advertisements
उत्तर
Given,
Height of the object, (h0) = 2 cm,
Height of the image, (h1) = 1 cm
distance between image and object, ( \[-\] u + v) = 40 cm 
We know that,
Magnification is given by:
\[m = \frac{h_i}{h_0} = \frac{v}{u}, \frac{1}{2} = \frac{v}{- u}\]
u = −2v
Using lens formula,
\[\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\]
\[ \Rightarrow \frac{1}{v} - \frac{1}{- 2v} = \frac{1}{f}\]
\[ \Rightarrow \frac{1}{v} + \frac{1}{2v} = \frac{1}{f}\]
\[ \Rightarrow f = \frac{2v}{3}\]
As per the question,
= −u + v = 40 cm,
= −(−2v) + v = 40 cm,
= 3v = 40 cm
\[v = 13 . 3 = \frac{40}{3} cm, u = \frac{80}{3}\]
∴ f = 8.9 cm
Hence, the required focal length is 8.9 cm and object distance is 26.66 cm.
APPEARS IN
संबंधित प्रश्न
Define the power of a lens.
(a) At what distance should the lens be held from the figure in order to view the squares distinctly with the maximum possible magnifying power?
(b) What is the magnification in this case?
(c) Is the magnification equal to the magnifying power in this case? Explain.
Name the physical quantity whose unit is dioptre.
How is the power of a lens related to its focal length?
Fill in the following blank with suitable words :
The reciprocal of the focal length in metres gives you the _________ of the lens, which is measured in ___________.
What is the unit of power of a lens? Define the unit of power of a lens.
Define the term focal length of a lens.
How is the power of a lens related to its focal length?
How is the sign (+ or -) of power of a lens related to its divergent or convergent action?
A thin converging lens is formed with one surface convex and the other plane. Does the position of image depend on whether the convex surface or the plane surface faces the object?
A symmetric double convex lens in cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens was 4 D, the power a cut-lens will be
Surabhi from std. X uses spectacle. The power of the lenses in her spectacle is 0.5 D.
Answer the following questions from the given information:
- Identify the type of lenses used in her spectacle.
- Identify the defect of vision Surabhi is suffering from.
- Find the focal length of the lenses used in her spectacle.
A lens forms an upright and diminished image of an object, irrespective of its position. What kind of lens is this? Draw an outline ray diagram to show the formation of the image. State the position and one more characteristic of the image.
A convex lens is of focal length 20 cm. Find its power.
If the lens is of focal length 25 cm. Calculate the power of the lens.
The power of the magnifying glass depends on the distance of the magnifying glass from object.
A point object is placed at O in front of a glass sphere as shown in figure.
Show the formation of the image by the sphere.
