Physics-
General
Easy

Question

Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength lambda passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is

  1. square root of fraction numerator 3 lambda D over denominator 2 end fraction end root    
  2. square root of lambda D end root    
  3. square root of fraction numerator lambda D over denominator 2 end fraction end root    
  4. square root of 3 lambda D end root    

The correct answer is: square root of fraction numerator lambda D over denominator 2 end fraction end root


    Path difference between the waves reaching atP comma capital delta equals capital delta subscript 1 end subscript plus capital delta subscript 2 end subscript
    wherecapital delta subscript 1 end subscript equals Initial path difference
    capital delta subscript 2 end subscript equalsPath difference between the waves after emerging from slits.

    capital delta subscript 1 end subscript equals S S subscript 1 end subscript minus S S subscript 2 end subscript equals square root of D to the power of 2 end exponent plus d to the power of 2 end exponent end root minus D
    and capital delta subscript 2 end subscript equals S subscript 1 end subscript O minus S subscript 2 end subscript O equals square root of D to the power of 2 end exponent plus d to the power of 2 end exponent end root minus D
    therefore capital delta equals 2 open curly brackets left parenthesis D to the power of 2 end exponent plus d to the power of 2 end exponent right parenthesis to the power of fraction numerator 1 over denominator 2 end fraction end exponent minus D close curly brackets equals 2 open curly brackets left parenthesis D to the power of 2 end exponent plus fraction numerator d to the power of 2 end exponent over denominator 2 D end fraction right parenthesis minus D close curly brackets
    equals fraction numerator d to the power of 2 end exponent over denominator D end fraction (From Binomial expansion)
    For obtaining dark at O, capital delta must be equals to left parenthesis 2 n minus 1 right parenthesis fraction numerator lambda over denominator 2 end fraction i.e. fraction numerator d to the power of 2 end exponent over denominator D end fraction equals left parenthesis 2 n minus 1 right parenthesis fraction numerator lambda over denominator 2 end fraction rightwards double arrow d square root of fraction numerator left parenthesis 2 n minus 1 right parenthesis lambda D over denominator 2 end fraction end root
    For minimum distance n equals 1 so d equals square root of fraction numerator lambda D over denominator 2 end fraction end root

    Related Questions to study

    General
    Physics-

    A monochromatic beam of light falls on YDSE apparatus at some angle (say theta) as shown in figure. A thin sheet of glass is inserted in front of the lower slit S2. The central bright fringe (path difference = 0) will be obtained

    A monochromatic beam of light falls on YDSE apparatus at some angle (say theta) as shown in figure. A thin sheet of glass is inserted in front of the lower slit S2. The central bright fringe (path difference = 0) will be obtained

    Physics-General
    General
    Chemistry-

    Given  The number of electrons present in l = 2 is

    Given  The number of electrons present in l = 2 is

    Chemistry-General
    General
    Maths-

    Plot A(3,-5) on a carteaion plane.

    Plot A(3,-5) on a carteaion plane.

    Maths-General
    parallel
    General
    Maths-

    If m is a non-zero number and integral subscript blank superscript blank fraction numerator x to the power of 5 m minus 1 end exponent plus 2 x to the power of 4 m minus 1 end exponent over denominator left parenthesis x to the power of 2 m end exponent plus x to the power of m plus 1 right parenthesis cubed end fraction equals f left parenthesis x right parenthesis plus c, then f(x) is:

    If m is a non-zero number and integral subscript blank superscript blank fraction numerator x to the power of 5 m minus 1 end exponent plus 2 x to the power of 4 m minus 1 end exponent over denominator left parenthesis x to the power of 2 m end exponent plus x to the power of m plus 1 right parenthesis cubed end fraction equals f left parenthesis x right parenthesis plus c, then f(x) is:

    Maths-General
    General
    Maths-

    The integral integral subscript blank superscript blank fraction numerator d x over denominator left parenthesis x plus 1 right parenthesis to the power of 3 divided by 4 end exponent left parenthesis x minus 2 right parenthesis to the power of 5 divided by 4 end exponent end fraction equal

    The integral integral subscript blank superscript blank fraction numerator d x over denominator left parenthesis x plus 1 right parenthesis to the power of 3 divided by 4 end exponent left parenthesis x minus 2 right parenthesis to the power of 5 divided by 4 end exponent end fraction equal

    Maths-General
    General
    Maths-

    If not stretchy integral subscript blank superscript blank fraction numerator 2 s i n x plus 3 c o s x over denominator blank c o s blank x left parenthesis s i n to the power of 2 end exponent x plus 2 c o s to the power of 2 end exponent x right parenthesis end fraction d x equals logvertical linef(x)vertical line plus lambda t a n to the power of negative 1 end exponent left parenthesis fraction numerator blank t a n blank x over denominator square root of 2 end fraction right parenthesis plus c comma then left parenthesis lambda f right parenthesis equals

    If not stretchy integral subscript blank superscript blank fraction numerator 2 s i n x plus 3 c o s x over denominator blank c o s blank x left parenthesis s i n to the power of 2 end exponent x plus 2 c o s to the power of 2 end exponent x right parenthesis end fraction d x equals logvertical linef(x)vertical line plus lambda t a n to the power of negative 1 end exponent left parenthesis fraction numerator blank t a n blank x over denominator square root of 2 end fraction right parenthesis plus c comma then left parenthesis lambda f right parenthesis equals

    Maths-General
    parallel
    General
    Maths-

    An incomplete frequency distribution is given below Median value is 46, the missing frequency is

    An incomplete frequency distribution is given below Median value is 46, the missing frequency is

    Maths-General
    General
    Physics-

    In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP

    In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP

    Physics-General
    General
    Physics-

    A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be

    A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be

    Physics-General
    parallel
    General
    Physics-

    A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio I m i n subscript m a x end subscript is

    A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio I m i n subscript m a x end subscript is

    Physics-General
    General
    Physics-

    AB is incident wave front on mirror R and mirror S whereas PQ and P ´ Q ´ is reflected wave front from mirror R and mirror S respectively. Choose the correct statement

    AB is incident wave front on mirror R and mirror S whereas PQ and P ´ Q ´ is reflected wave front from mirror R and mirror S respectively. Choose the correct statement

    Physics-General
    General
    Physics-

    In the diagram shown, the separation between the slit is equal to 3 lambda comma where lambda is the wavelength of the light incident on the plane of the slits A thin film of thickness 3 lambda and refractive index 2 has been placed in the front of the upper slit. Assuming D greater than greater than lambda the distance of the central maxima on the screen from O is:

    In the diagram shown, the separation between the slit is equal to 3 lambda comma where lambda is the wavelength of the light incident on the plane of the slits A thin film of thickness 3 lambda and refractive index 2 has been placed in the front of the upper slit. Assuming D greater than greater than lambda the distance of the central maxima on the screen from O is:

    Physics-General
    parallel
    General
    Physics-

    Three weight A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)

    Three weight A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)

    Physics-General
    General
    Physics-

    As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be

    As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be

    Physics-General
    General
    Physics-

    Figures I, II, III and IV depict variation of force with time
    I) 
    II) 
    III) 
    IV) 
    The impulse is highest in the case of situations depicted. Figure

    Figures I, II, III and IV depict variation of force with time
    I) 
    II) 
    III) 
    IV) 
    The impulse is highest in the case of situations depicted. Figure

    Physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.