An isotropic point source of light is suspended h metre vertically above the centre of the circular table of radius r metre. Then, the ratio of illumenances at the centre to that at the edge of the table is

$1 + (\frac{r^{2}}{h^{2}})$

$1 + (\frac{h^{2}}{r^{2}})$

${\{1 + \frac{r^{2}}{h^{2}}\}}^{3 / 2}$

${\{1 + \frac{h^{2}}{r^{2}}\}}^{3 / 2}$

Solution

${\{1 + \frac{r^{2}}{h^{2}}\}}^{3 / 2}$

According to the question, the situation is shown in the figure below,

$E_{1} = \frac{I}{(LO)^{2}} = \frac{I}{h^{2}} . . . (i)$

The illumination at the edge A is given by

$E_{2} = \frac{I \cos θ}{(LA)^{2}} = \frac{I \cos θ}{(h^{2} + r^{2})} . . . . (ii) From figure, \cos θ = \frac{h}{\sqrt{(h^{2} + r^{2})}} ∴ E_{2} = \frac{Ih}{(h^{2} + r^{2})^{3 / 2}} Dividing eq (i) by eq (ii), we get \frac{E_{1}}{E_{2}} = \frac{I / h^{2}}{Ih / (h^{2} + r^{2})^{3 / 2}} = \frac{(h^{2} + r^{2})^{3 / 2}}{h^{3}} = \frac{(h^{2} + r^{2})^{3 / 2}}{h^{2}} = {(1 + \frac{r^{2}}{h^{2}})}^{3 / 2}$

Some More Questions From Dual Nature of Radiation and Matter Chapter

If I₀ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives straight line whose slope

For Daily Free Study Material Join wiredfaculty

Dual Nature Of Radiation And Matter

Some More Questions From Dual Nature of Radiation and Matter Chapter

If I₀ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives straight line whose slope

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Dual Nature Of Radiation And Matter

An isotropic point source of light is suspended h metre vertically above the centre of the circular table of radius r metre. Then, the ratio of illumenances at the centre to that at the edge of the table is 1 + r2h2 1 + h2r2 1 + r2h23/2 1 + h2r23/2

Some More Questions From Dual Nature of Radiation and Matter Chapter

If I0 is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives straight line whose slope

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If I₀ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?