Answer:
The wavelength is [tex]\lambda_2 = 534 *10^{-9} \ m[/tex]
Explanation:
From the question we are told that
  The wavelength of the first light is  [tex]\lambda _ 1 = 587 \ nm[/tex]
  The order of the first light that is being considered is  [tex]m_1 = 10[/tex]
   The order of the second light that is being considered is  [tex]m_2 = 11[/tex]
Generally the distance between the fringes for the first light is mathematically represented as
   [tex]y_1 = \frac{ m_1 * \lambda_1 * D}{d}[/tex]
 Here  D is the distance from the screen
 and   d  is the distance of separation of the slit.
   For the second light the distance between the fringes is  mathematically represented as
     [tex]y_2 = \frac{ m_2 * \lambda_2 * D}{d}[/tex]
Now given that both of the light are passed through the same double slit
    [tex]\frac{y_1}{y_2} = \frac{\frac{m_1 * \lambda_1 * D}{d} }{\frac{m_2 * \lambda_2 * D}{d} } = 1[/tex]
=> Â Â [tex]\frac{ m_1 * \lambda _1 }{ m_2 * \lambda_2} = 1[/tex]
=> Â Â [tex]\lambda_2 = \frac{m_1 * \lambda_1}{m_2}[/tex]
=> Â Â [tex]\lambda_2 = \frac{10 * 587 *10^{-9}}{11}[/tex]
=> Â [tex]\lambda_2 = 534 *10^{-9} \ m[/tex]
