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 electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is $\lambda_e$,which of the following statement$(s)$ is(are) true?

• A
  $\lambda_e$ decreases with increase in $\phi$ and $\lambda_{\text{ph}}$
• B
  $\lambda_e$ is approximately halved,if $d$ is doubled
• C
  For large potential difference $(V \gg \phi / e)$,$\lambda_e$ is approximately halved if $V$ is made four times
• D
  $\lambda_e$ increases at the same rate as $\lambda_{\text{ph}}$ for $\lambda_{\text{ph}} < hc / \phi$