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The wavelength of the second light is ${位}_b=350\text{nm}$

The diffraction minimum of first light for second order is $m_a=2$.

The diffraction minimum of first light for third order is$m_a=3$

The diffraction is the phenomenon in which the light bends on the edges of the slit and pattern of light is formed on a screen.

The wavelength of first light is given as:

$m_1{位}_a=m_2{位}_b$

Here, $m_1$ is the first order of diffraction minimum for first light and role="math" localid="1663144017967" $m_2$ is the second order of diffraction minimum for second light

Substitute all the values in equation.

$$\begin{gathered} \left(1\right){位}_a=\left(2\right)\left(350\text{nm}\right) \\ {位}_a=700\text{nm} \end{gathered}$$

Therefore, the wavelength of first light is $700\text{nm}$.

(b)

The order of the diffraction minima of second light is given as:

$m_a{位}_a=m_b{位}_b$

Substitute all the values in equation.

$$\begin{gathered} \left(2\right)\left(700\text{nm}\right)=m_b\left(350\text{nm}\right) \\ {m}_b=4 \end{gathered}$$

Therefore, the order of diffraction minima for second light is width="8" height="15" role="math">4.

(c)

The order of the diffraction minima of second light is given as:

$m_a{位}_a=m_b{位}_b$

Substitute all the values in equation.

$$\begin{gathered} \left(3\right)\left(700\text{nm}\right)=m_b\left(350\text{nm}\right) \\ {m}_b=6 \end{gathered}$$

Therefore, the order of diffraction minima for second light islocalid="1663144938596" $6$.