Thin film interference: why is the thinnest film for maximum reflected light λ/2 not λ/4?

[Any Help]

Homework Statement

Monochromatic light, at normal incidence, strikes a thin film in air. If λ denotes the wavelength in the film, what is the thinnest film in which the reflected light will be a maximum?

• 
  
  A
  
  λ/4
• 
  
  B
  3λ/4
• 
  
  C
  λ
• 
  D
  
  much less than λ
• 
  
  E
  
  λ/2

Homework Equations

n air ∠ n glass
so at the first reflection it will cuase a 180° ray out of phase while the second ray reflected from the inside it will stay inphase because n air ∠ n glass
so for constructive interference: 2L=odd number*λ/2

The Attempt at a Solution

least odd number is one , so L=λ/4 ?? why it is incorrect

 

[TSny]

Your answer of λ/4 is correct. The problem statement does not mention glass.

 

[Cutter Ketch]

Well all I can do is sympathize. 1/4 should have been correct. Perhaps they have in mind a low index film on a high index substrate? Or perhaps the problem setter forgot about the 180 phase shift front to back and just got it wrong.

 

[NascentOxygen]

the thinnest film in which the reflected light will be a maximum[/color] minimum[/color] ?

possibly intended