Question:
The shape of the interference fringes in Young's double-slit experiment, when the distance between the slit and the screen is very large as compared to the slit separation, is nearly
The shape of the interference fringes in Young's double-slit experiment, when the distance between the slit and the screen is very large as compared to the slit separation, is nearly
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Remember the statement:
\[
\text{Actual shape} = \text{Hyperbolic},
\qquad
\text{Observed shape} = \text{Nearly straight}
\]
because in YDSE, the screen is placed very far from the slits.
Updated On: Jul 2, 2026
- straight
- parabolic
- circular
- hyperbolic
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The Correct Option is A
Solution and Explanation
Concept:
In Young's Double-Slit Experiment (YDSE), two coherent sources produce an interference pattern on a screen. The locus of points having a constant path difference is actually a hyperbola because the difference of distances from two fixed points remains constant.
However, in practical situations, the screen is placed at a very large distance compared to the separation between the slits. Under this condition, the rays reaching the screen are almost parallel and the hyperbolic fringes appear as straight lines.
Thus, the actual shape of the fringes is hyperbolic, but under the approximation
\[
D\gg d,
\]
where
\[
D=\text{distance of screen from slits}
\]
and
\[
d=\text{separation between slits},
\]
the fringes become nearly straight and equally spaced.
Step 1: Understand the actual geometry of interference fringes.
The path difference at any point on the screen is \[ \Delta = S_2P-S_1P. \] The set of all points for which \(\Delta\) is constant forms a hyperbola. Therefore, theoretically, the interference fringes are hyperbolic.
Step 2: Apply the practical approximation used in YDSE.
In the experiment, \[ D\gg d. \] Under this condition, only a small portion of the hyperbola is observed on the screen and it appears almost as a straight line. Hence, the fringes are nearly straight. \[ \boxed{\text{Shape of fringes }=\text{ Straight}} \]
Step 1: Understand the actual geometry of interference fringes.
The path difference at any point on the screen is \[ \Delta = S_2P-S_1P. \] The set of all points for which \(\Delta\) is constant forms a hyperbola. Therefore, theoretically, the interference fringes are hyperbolic.
Step 2: Apply the practical approximation used in YDSE.
In the experiment, \[ D\gg d. \] Under this condition, only a small portion of the hyperbola is observed on the screen and it appears almost as a straight line. Hence, the fringes are nearly straight. \[ \boxed{\text{Shape of fringes }=\text{ Straight}} \]
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