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I am attempting the following question:

1. Homework Statement

1. Homework Statement

If the extinction in the infra-red K-band (filter central wavelength = 2.13 micrometres) is 10 times less than it is in the optical V-band (filter central wavelength = 550 nanometres), what affect would a cloud of Av = 3 have on the flux density observed in V and K if the stars intrinsic V-band apparent magnitude is 12?

## Homework Equations

(i) m

_{1}-m

_{2}=-2.5log(F

_{1}/F

_{2})

(ii) m

_{vobs}-m

_{vo}=A

_{v}

(iii) F

_{λ}=F/Δλ

(iv) E(K-V)=(K

_{obs}-V

_{obs})-(K

_{o}-V

_{o})

(v) E(K-V)=A

_{k}-A

_{v}

A

_{v}=3

m

_{vo}=12

## The Attempt at a Solution

OK,

So I know that to start things off, A

_{k}is 10 times less than A

_{v}so A

_{k}=0.1*A

_{v}=0.3. Using this, I can calculate the value of E(K-V) using the known value of A

_{v}and equation (v) to get E(K-V)=-2.7.

I can get the ratio of fluxes from the V-band quite easily, knowing I have the intrinsic apparent magnitude (m

_{vo}), I can rearrange equation (ii) to see that the observed apparent magnitude in the V band (m

_{vobs}) is 15 (12+3).

From here I can simply plug into equation (i) and rearrange for the flux ratio (F

_{vobs}/F

_{vo}) = 0.063

I can also use equation (iv) and the calculated value of E(K-V) to rearrange for m

_{kobs}-m

_{ko}to get this value to = 0.3.

Again, from here I can calculate the ratio of fluxes in the K-band using equation (i) again to find that (F

_{kobs}/F

_{ko})=0.759.

First of all, I am assuming that this is the right approach and if it is then I am stuck as to what to do next.

Is this as simple as then looking at the ratio of fluxes and multiplying by ΔF

_{λ}?

Am I right in assuming that ΔF

_{λ}is simply 2.13μm-0.55μm=1.58μm?

Any pointers gratefully received!