Advertisements
Advertisements
प्रश्न
Obtain the equation for resolving the power of the microscope.
Advertisements
उत्तर
- A microscope is used to see the details of the object under observation. The ability of a microscope depends not only in magnifying the object but also in resolving two points on the object separated by a small distance dmin. Smaller the value of dmin better will be the resolving power of the microscope.
Resolving power of microscope
`"r"_0 = (1.22 lambda "v")/"a"` - then the magnification m is,
m = `"r"_0/"d"_"min"`
`"d"_"min" = "r"_0/"m" = (1.22 lambda"v")/"am" = (1.22 lambda "v")/("a"("v"//"u")) = (1.22 lambda"u")/"a"`
[∴ m = v/u]
`"d"_"min" = (1.22 lambda "f")/"a"` [∴ u ≈f]
On the other side,
2 tan β ≈ 2 sin β = `"a"/"f"` ∴ [a = f 2sin β]
`"d"_"min" = (1.22 lambda)/(2 sin beta)` - To further reduce the value of dmin the optical path of the light is increased by immersing the objective of the microscope into a bath containing oil of refractive index n.
`"d"_"min" = (1.22 lambda)/(2"n" sin beta)` - Such an objective is called oil-immersed objective. The term n sin β is called numerical aperture NA.
`"d"_"min" = (1.22 lambda)/(2 ("NA"))`
APPEARS IN
संबंधित प्रश्न
Answer the following question in detail.
How does magnifying power differ from linear or lateral magnification?
Answer the following question in detail.
Derive an expression for the magnifying power of a simple microscope. Obtain its minimum and maximum values in terms of its focal length.
Answer the following question in detail.
What is a terrestrial telescope and an astronomical telescope?
Answer the following question in detail.
What is the limitation in increasing the magnifying powers of a compound microscope?
Discuss about simple microscope and obtain the equations for magnification for near point focusing and normal focusing.
What is the near point focusing?
Why is oil-immersed objective preferred in a microscope?
What are the advantages and disadvantages of using a reflecting telescope?
What is the use of an erecting lens in a terrestrial telescope?
What is the use of collimator in a spectrmeter?
What are the uses of spectrometer?
A compound microscope has a magnifying power of 100 when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. What is the focal length of the eyepiece.
The near point and the far point for a person are 50 cm and 500 cm, respectively. Calculate the power of the lens the person should wear to read a book held in hand at 25 cm. What maximum distance is clearly visible for the person with this lens on the eye?
A light wave of wavelength λ is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at a distance D. If linear width of the principal maxima is equal to the width of the slit, then the distance D is
When a convex lens of 12.5 cm focal length is used as a magnifying glass, normal eye can see an object clearly at a distance of 25 cm. The magnifying power of the instrument is ____________.
The magnifying power of a telescope is nine. When it is adjusted for parallel rays, the distance between the objective and eyepiece is 20 cm. The focal length of objective and eyepiece are respectively.
The magnifying power of a telescope is high if its objective and eyepiece have respectively ______.
The speed of light in media 'A' and 'B' are 2.0 × 1010 cm/s and 1.5 × 1010 cm/s respectively. A ray of light enters from medium B to A at an incident angle 'θ'. If the ray suffers total internal reflection, then ______.
An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to ______ cm.
