Number of images formed by two inclined mirror
When two mirrors are put at an angle θ, find the number of images by
- 360/θ
- but when the result after division is even , required answer is ( 360 /θ -1), except for the condition when object is placed at bisector
- round off if the result is fraction
Focal length is –ve for
- convex mirror
- for concave lens.
Deviation by plane mirror , δ = 180 -2i
Deviation by two plane mirror inclined at angle θ , δ = 360 – θ
δ= A (µ -1 )
Angular dispersion (θ)= A ( µv - µR )
W = (µv - µR / µ -1)
Longitudinal magnification = ( Trans. Magnification )2
If any one face of equiconvex lens is silvered,
Feq = R / 2 (2µ -1)
If plane face of planoconvex lens is silvered,
F = R/2(µ-1)
If curved face of planoconvex lens is silvered,
f=R/µ
distance of nth image from both mirror = 2nd where d is distance of two mirror
Example question:
distance of 4 th image from the first mirror with mirror separation 10 cm.
- then as 4 is even,
- Solution:
- nd – object distance of own mirror
- = 4 * 10 – object distance of own mirror
Q) If odd then ( in place of 4 odd number given )
Ans= > nd – object distance of opposite mirror
Here, I= displacement of Image, O= Displacement of Object, M= Displacement of mirror
Relative velocity of image ith respect to object and image with respect to mirror.
VIO =2(V0+ Vm)
VIM = V0 + Vm
Minimum distance between object and real image in case of concave mirror is zero and between object and real image for convex lens is 4F.
µwater=4/3 =1.33
µglass = 5/3 = 1.67
Bird and pond problem,
Distance of fish by bird = h + x/µ ( h= height of bird from the pond, )
Distance of bird by fish = µh + x (x = depth of the pond in fish)
Radius of circle immersing out = h/√(µ2
Convex mirror only forms erect and diminished image.
1.µ(refractive index) increases = ρ(density) increases = v(velocity) increases
2.T(temperature ) decreases = λ(wave length) decrease= C(critical angle) increases
| Microscopes or telescopes | Near | far |
| 1.simple microscope | M=(D/fe +1) | M= D/fe |
| 2.compound microscope | M= (D/fe + 1)*V0/U0 | M = D/fe *V0/U0 |
| 3.Telescope | M= (1 + fe/D)* f0/fe | M= f0/fe |
Chromatic aberration does not occur in spherical mirror.
Concave mirror is used for shaving and make up and convex mirror is used in cars, bikes and bus.
W1/W2 = -f1/f2 ( achromatism )
Shift = t(1-1/µ)
µ = 1/sinC
1/√(µ0Ԑ0 ) = 3 * 108 m/s =C
µ = sin((A+δm)/2) / (sin A/2)
Lens cut perpendicular to principal axis,
Intensity same, focal length doubled and power halved.
Lens cut along principle axis
intensity half , focal length and power same.
Two thin lenses separated by distance x is,
1/feq = 1/f1 + 1/f2 – x/f1f2
Defect of lens,
Myopia = short sightness
Hypermetropia = long sightness
1/f = (1/ can’t see ) – (1/ can see)
Eg, man can’t see object beyond 100cm what is the focal length and power of lens required to correct the defect.
1/ f = 1/infinity – 1/100
Therefore, f= -100cm
F =- 1 D
Fizeau’s method = 4mnd
Focault’s method = 4mnd/θ
Michelson’s method = C = 8nd
fringe width
β = λD/d
for, nth dark fringe, Yn= (2n-1)λD/2d
for nth bright fringe , Yn= nλD/d
Brewster’s law
µ = tanθi
R = radiant flux ( watt) --> total energy emitted per second
Ø = luminous flux (lumen) ---> visible energy emitted per second
L = luminous intensity (candela)----> power of source
I= illiuminance (lux)----> brightness of source
1 lumen = 1/685 watt
1 lux = 10-4 phot
L =Ø / solid angle
I = L /r2
Luminous efficiency (ŋ)=Ø / R x 100%
Time of expose of camera = (f/d)2 (f= focal length of lens , d= diameter of lens)
It = constant ( t= time of exposure)
Resolving power of telescope = 1/ dθ = D /1.22λ
Dθ ----> angular separation
D -----> aperture of telescope