Light of wavelength $\lambda_{\text {ph }}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $\phi$ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrode. If the minimum de Broglie wavelength of the electrons passing through the anode is $\lambda_{\mathrm{e}}$, which of the following statement(s) is (are) true?
Select the correct option:
A
$\lambda_{\mathrm{e}}$ decreases with increase in $\phi$ and $\lambda_{\mathrm{ph}}$
B
$\lambda_{\mathrm{c}}$ is approximately halved, if d is doubled
C
For large potential difference $(\mathrm{V} \gg \phi / \mathrm{e}), \lambda_0$ approximately halved if V is made four times
D
$\lambda_e$ increases at the same rate as $\lambda_{n b}$ for $\lambda_{n b}<\mathrm{hc} / \phi$
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