The phases of the light wave at c, d, e and f are respectively. It is given that [2007]

Question

The figure shows a surface XY separating two transparent media, medium-1 and medium-2. The lines ab and cd represent wavefronts of a light wave travelling in medium-1 and incident on XY. The lines ef and gh represent wavefronts of the light wave in medium-2 after refraction. [2007]

Q. The phases of the light wave at $c, d, e$ and $f$ are $ϕ_{c}$ , $ϕ_{d}$ , $ϕ_{e}$ and $ϕ_{f}$ , respectively. It is given that $ϕ_{c} \neq ϕ_{f} .$

Smart Achievers · Accepted Answer

(3)

Since points $c$ and $d$ are on the same wavefront,

$∴$ $ϕ_{d} = ϕ_{c}$

Similarly, $ϕ_{e} = ϕ_{f}$

$∴$ $ϕ_{d} - ϕ_{f} = ϕ_{c} - ϕ_{e}$

Solution

1 $ϕ_{c}$ cannot be equal to $ϕ_{d}$

2 $ϕ_{d}$ can be equal to $ϕ_{e}$

3 $(ϕ_{d} - ϕ_{f})$ is equal to $(ϕ_{c} - ϕ_{e})$

4 $(ϕ_{d} - ϕ_{c})$ is not equal to $(ϕ_{f} - ϕ_{e})$

Ans.
(3)

Since points $c$ and $d$ are on the same wavefront,

$∴$ $ϕ_{d} = ϕ_{c}$

Similarly, $ϕ_{e} = ϕ_{f}$

$∴$ $ϕ_{d} - ϕ_{f} = ϕ_{c} - ϕ_{e}$

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Solution

1 ϕc cannot be equal to ϕd

2 ϕd can be equal to ϕe

3 (ϕd-ϕf) is equal to (ϕc-ϕe)

4 (ϕd-ϕc) is not equal to (ϕf-ϕe)