Ducting - novice query

Hiya We've had some water drip into the light in our bathroom. I've investigated the loft where the ducting for the extractor fan was twisted round and I think where the ducting met the outside vent was working loose as water pooled.
I've reduced the ducting and made it straight but it doesn't connect well. I think the roof vent ducting is wider than the extractor ducting. I presume the extractor ducting is supposed to go over the roof one and then be fixed? Can I just use a reducer for this to connect the wider to the narrower ducting? Or do I need wider ducting ?
Sorry I'm a complete novice at DIY!

Duct tape.

It would be useful to measure the internal diameter of the two ducting parts. I suspect the white duct from the extractor is 100mm and the grey roof duct is 110mm. You could fit a 100mm straight round pipe connector or a short length of 100mm pipe between them, but may have to pad the 110mm duct out a bit. Use a Tyrap around the white ducting to hold it securely. Wrap some insulation around the ducting to reduce potential condensation.

Thanks yes you're right 100mill the white and a little larger the grey. I'm getting a pipe connector tomorrow so will try as you say and see if I can join th effectively that way.
I think ultimately though I need to get someone to put in a new solid pipe rather than flex to vent straight out horizontally. I think that should work better and stop any condensation falling back in. I'll see if I can get someone to have a look at for me. Thanks for the help

The spiral band on the white ducting makes it a bit difficult to seal it to the grey. However, you can carefully half lap wrap some Denso tape around the white one using the inner spiral wire for some support and then continue up over the grey pipe. Once you have wrapped it around the grey section a couple of turns you can then work back down over the white ensuring there are no gaps. Once wrapped gently compress the tape with smoothing actions, (such as used when having a plaster cast fitted), to ensure it bonds all around.