In a Young's double slit experiment, it is desired to modify the...

Let the initial angular fringe width be $\theta$ and the initial linear fringe width be $\beta$.

The new angular fringe width is $\theta' = 1.5 \theta$.
The new linear fringe width is $\beta' = 3 \beta$.

The linear fringe width is given by $\beta = \theta D$, which implies the screen distance is $D = \dfrac{\beta}{\theta}$.

The new screen distance required is:
$D' = \dfrac{\beta'}{\theta'} = \dfrac{3 \beta}{1.5 \theta} = 2 \left(\dfrac{\beta}{\theta}\right) = 2 D$

Thus, the screen distance must be doubled.

The angular fringe width is given by $\theta = \dfrac{\lambda}{d}$.
To achieve $\theta' = 1.5 \theta$, we can either increase the wavelength $\lambda$ by $50\%$ (so $\lambda' = 1.5 \lambda$) or decrease the slit separation $d$ by $33.3\%$.

Therefore, increasing the wavelength by $50\%$ and doubling the screen distance will produce the desired changes.

Answer: Increase the wavelength by $50\%$ and double the screen distance.