In the figure, light is incident on a thin lens as shown. The radius of curvature for both the surfaces is R. Determine the focal length of this system.

In the figure, light is incident on a thin lens as shown. The radius o

1.	In the figure, light is incident on a thin lens as shown. The radius of curvature for both the surfaces is R. Determine the focal length of this system.
Answer» (i) For refraction at the first surface of the lens Here, `u = - oo, R = + R` Suppose the first surface converges the incident parallel beam at a distance `v_(1)`, assuming medium `mu_(2)` to be continuous. As `-(mu_(1))/(u) + (mu_(2))/(v) = (mu_(2) - mu_(1))/(R )` `:. -(mu_(1))/(-oo) + (mu_(2))/(v_(1)) = (mu_(2)-mu_(1))/(R )` or `(mu_(2))/(v_(1)) = (mu_(2) - mu_(1))/(R )` ...(i) (ii) For refraction at second surface of the lens `-(mu_(2))/(u) + (mu_(3))/(v) = (mu_(3) - mu_(2))/(R )` ...(ii) The image formed by the first surface acts as virtual object for the second surafce and this second surface forms the image at the focus of the lens. `:. u = v_(1), v = + f and R = + R` From (ii), `-(mu_(2))/(v_(1)) + (mu_(3))/(+f) = (mu_(3) - mu_(2))/(R )` ...(iii) Adding (i) and (ii), we get `(mu_(3))/(f) = (mu_(2) - mu_(1))/(R ) + (mu_(3) - mu_(2))/(R ) = (mu_(3) - mu_(1))/(R )` `f = (mu_(3)R)/(mu_(3) - mu_(1))`

Discussion

No Comment Found

Related InterviewSolutions

Red light of wavelength `6500 Å` from a distant source falls on a slit `0.50 mm` wide. Calculate the distance between first two dark bands on each side of central bright band in the diffraction pattern observed on a screen placed `1.8 m` from the slit.
The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre is
The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre isA. `2`B. `1//2`C. `4`D. `16`
Among the two interfering monochromatic sources A and B, A is ahead of B in phase by `66^@`. If the observation be taken from point P, such that `PB-PA=lambda//4`. Then the phase difference between the waves from A and B reaching P isA. `156^(@)`B. `140^(@)`C. `136^(@)`D. `126^(@)`
The radius of curvature of curved surface of a thin plano-convex lens is `10 cm` and the refractive index is `1.5`. If the plano surface is silvered, then the focal length will be.A. 15 cmB. 20 cmC. 5 cmD. 10 cm
Calculate the resolving power of a microscope with cone angle of light falling on the objective equal to `60^(@)`. Take `lambda = 600 nm mu` for air `= 1`.
The diameter of the pupil of human eye is about `2 mm`. Human eye is most sensitive to the wavelength `555 nm`. Find the limit of resolution of human eye.
Assume that light of wavelength `6000 Å` is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of 100 inch ? (NCERT Solved example)
A central fringe of interference pattern produced by light of wavelength `6000 Å` is shifted to the position of 5th bright fringe by introducing thin film of `mu = 1.5`. Calculate thickness of the film.
Laser light of wavelength `630 nm` incident on a pair of slits produces an interference pattern where bright fringes are separated by `8.1 mm`. Another light produces the interference pattern, where the bright fringes are separated by `7.2 mm`. Calculate the wavelength of second light.

In the figure, light is incident on a thin lens as shown. The radius of curvature for both the surfaces is R. Determine the focal length of this system.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment