JEE MAIN CHAPTER OVERVIEW
Chapter Priority | 3 (LOW) |
Number of problems in PYQ | HIGH |
Difficulty | MODERATE/HIGH |
To solve JEE MAIN problems for Optical Instruments, you need to remember all formulae given in these notes.
Note: If you don't remember the formulae for special cases given in these notes, problems in the exam will take a lot of time and will become calculation heavy.
For the magnifying power formula given below, use magnitudes only without signs, wherever required a '-' sign has been added to the formula.
KEY CONCEPTS FOR JEE MAIN
Least Distance of Distinct Vision
It is the minimum distance at which the object must be kept for the clear vision. This distance is called least distance of distinct vision (+D).
Our eyes find it hard to view objects that are kept closer than least distance of distinct vision.
For normal eyes, it is 25 cm.
Least distance of distinct vision is also called NEAR POINT or point of STRESSED VISION.
FAR POINT
When eyes are focussing on a distant object (i.e. at infinity) the eye muscles are relaxed and focal length of eye lens is maximum. Image of the object is formed on the retina without strain on the eyes. We can see the object clearly.
So, infinity is also the FAR POINT of a normal eye or point of RELAXED VISION. When image is formed at infinity, it is called NORMAL ADJUSTMENT.
VISUAL ANGLE
Image of an object formed on the retina is proportional to the angle subtended by the object on the eye. This angle is called the visual angle.
Optical instruments artificially increase this angle for us to see the objects clearly.
MAGNIFYING POWER of a MICROSCOPE
The magnifying power is the factor by which the image on the retina can be enlarged by using the microscope. It is also called ANGULAR MAGNIFICATION.
Magnifying power of a microscope is the ratio of the visual angle subtended by the image on the eye to the angle subtended by the object if the object was kept at least distance of distinct vision.
Remember, it is not necessary that the object is kept at least distance of distinct vision for us to calculate magnifying power. We can keep the object anywhere and calculate angle subtended by image. But we always divide by the angle subtended by the object if kept at least distance of distinct vision.
Following cases will enhance your understanding:
MAGNIFYING POWER OF A SIMPLE MICROSCOPE
1. GENERAL FORMULA
u0 is the object distance when the object is kept between focus and eye(lens)
v0 is the image distance
D is the least distance of distinct vision
h is the height of the object
2. NORMAL ADJUSTMENT (i.e. image is formed at infinity)
f is the focal length of the lens
For image to be formed at infinity, the object must be kept at focus. In the general formula given above, replace object distance by focal length.
3. NEAR POINT OR STRESSED VISION ADJUSTMENT
Image is formed at the least distance of distinct vision.
For a simple microscope, magnifying power (m) lies between normal adjustment (D/f) and stressed vision adjustment (1 + D/f)
D/f < m < (1+ D/f)
COMPOUND MICROSCOPE
It consists of two converging lenses arranged coaxially. The one facing the object is called objective and the one close to the eye is called the eyepiece or ocular. The objective has a smaller aperture and smaller focal length than those of the eyepiece.
Magnification by a compound microscope is a two-step process. In the first step, the objective produces a magnified image of the given object. In the second step, the eyepiece produces an angular magnification.
The overall angular magnification is the product of the two magnifications produced by the objective and the eyepiece.
1. NEAR POINT/ STRESSED VIEW (final image @ near point)
In the above general formula for near point adjustment, certain approximations can be made -
V0 = L (as focal length of objective is small and objective image is formed near eyepiece)
The above approximation also implies that V0/U0 = L/f0 (try proving this with lens formula, fobjective << V0 )
In this case, the general formula for near point adjustment becomes:
2. NORMAL ADJUSTMENT/ RELAXED VISION
In this case, the image is formed at infinity.
ASTRONOMICAL TELESCOPE
Definition of magnifying power of telescope is different from that used for a microscope.
For a telescope,
[NOTE: The denominator for telescope is the angle subtended by the object which is different from that for a microscope in which the denominator was angle subtended by object if object kept at least distance for distinct vision].
1. Normal Adjustment, when image is formed at infinity
2. Stressed vision (final image formed at near point)
Hope you can REVISE OPTICAL INSTRUMENTS FOR JEE MAIN PHYSICS from this guide to answer all varieties of JEE MAIN PYQs.
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