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Ray Optics and Optical Test - 26

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Ray Optics and Optical Test - 26
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  • Question 1
    1 / -0
    Why are red coloured lights are used in traffic signals to stop the vehicles?
    Solution
    We know among the seven colours of white light, red colour has maximum wavelength. That is why red colour is least scattered by atmospheric dust and other particles. Hence red colour is used to indicated any danger sign.
  • Question 2
    1 / -0
    The colour which has least critical angle is
    Solution
     For total internal reflection to take place. μsinθc=1θc=sin1(1μ)\begin{array}{l}\text { For total internal reflection to take place. } \\\qquad \begin{array}{l}\mu\sin\theta_{c}=1 \\\theta_{c}=\sin ^{-1}\left(\frac{1}{\mu}\right)\end{array}\end{array}
     As a fact, the refractive index for a ray is inversely  proportional to its wavelength. \begin{array}{l}\text { As a fact, the refractive index for a ray is inversely } \\\text { proportional to its wavelength. }\end{array}
    μ×1λ Since violet has shortest wavelength it’s critical  angle is also low \begin{array}{l}\quad \mu \times \frac{1}{\lambda} \\\text { Since violet has shortest wavelength it's critical } \\\text { angle is also low }\end{array}
  • Question 3
    1 / -0
    A bird is flying 12m12 m above the surface of a pond. What is the apparent position of the bird as viewed by a fish 1m1m below the surface? (aμw=43_{a}\mu _{w}=\cfrac{4}{3})
    Solution
    h=12 m,h=?h=12 \ m , h'=?

     aμw=43,d=1m_a\mu_w=\dfrac{4}{3} , d=1m  

    aμw=hh1:43=h12_a\mu_w=\dfrac{h'}{h_1} : \dfrac{4}{3}=\dfrac{h}{12}

    h=43×12=16m h'=\dfrac{4}{3}\times12=16m 

    Total height =h+d=(16+1)m=17m=h'+d=(16+1)m=17m
  • Question 4
    1 / -0
    The bending of light as it passes from one medium into another is commonly known as
    Solution
    In refraction ray of light passes from one medium to another medium. The ray of light bends towards normal in the denser medium.

  • Question 5
    1 / -0
    ABCD represents a glass slab and PQRS indicates the path of a light ray passing through the slab.If the refractive index of the glass is 3\sqrt{3}, find 'x'.

    Solution
    Given r = 30 degree. Since r.i = 3 \sqrt 3. using μ=sini/sinr \mu = sin i / sin r , we get i = 60 degree.
    Now lateral shift = thickness ×\times sin (i - r) / cos r = 15  ×\times (1/2) (2 / 3)=53 \sqrt 3) = 5 \sqrt 3
  • Question 6
    1 / -0
    A bird flying above a pond starts moving vertically down towards the water below at a speed of v m s1v \ m  s^{-1}. Find its apparent velocity as viewed by a fish located at a depth of dd m below the surface of water of refractive index μ\mu .
    Solution
    As the refractive index, μ=\mu=apparent distance/true distance=apparent velocity/true velocity.
    So, apparent velocity is μ×\mu\times true velocity=μ×v=μv\mu\times v=\mu v
  • Question 7
    1 / -0
    When light travels from one medium into another it suffers
    Solution
    When light travels from one medium into another it suffers refraction,
  • Question 8
    1 / -0
    The figure shows cross section of a hollow glass tube of internal radius rr, external radius RR and index of refraction nn. For two rays DE and ABC (in which DE lies on ODE and DE is parallel to BC), the separation r1r_1 will be :

    Solution


    In given figure θ\theta is angle of refraction and α\alpha is angle of incidence for ray ABC.

    Required length = r1=BPr_1=BP

    Since DEBC    BOP=θDE\parallel BC\implies \angle BOP=\theta 

    Now, in ΔBOP:\Delta BOP:-

         r1=BP=OBsinθ=Rsinθr_1=BP=OB\sin\theta=R\sin \theta

        sinθ=r1R\implies \sin\theta=\dfrac{r_1}{R}

    In ΔOAB:\Delta OAB:-
     
    A=90o\angle A=90^{o}
    sinα=rR\sin \alpha=\dfrac{r}{R}

    Now, at refraction of ray ABCABC

    sinθsinα=n\dfrac{\sin\theta}{\sin\alpha}=n

        r1/Rr/R=n    r1r=n\implies \dfrac{r_1/R}{r/R}=n\implies \dfrac{r_1}{r}=n

        r1=nr\implies r_1=nr

    Answer-(C)

  • Question 9
    1 / -0
    A beam of light consisting of red, green and blue is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will
    Solution
    At point A, for total internal reflection to take place, μ sin i>1\mu \ sin \ i > 1
    Hence μ>2\mu>\sqrt{2} for total internal reflection to take place,
    Thus green and blue colours suffer total internal reflection whereas red just refracts and gets separated from the other two.

  • Question 10
    1 / -0
    A thin lens with focal length f to be used as magnifying glass. Which of the following statements regarding the situation is true?
    Solution
    A converging lens, magnifies the image of an object if it is placed at a distance less than the focal length of the lens.
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